Load balancing computational methods in a short-code spread-spectrum communications system

ABSTRACT

The invention provides methods and apparatus for multiple user detection (MUD) processing that have application, for example, in improving the capacity CDMA and other wireless base stations. One aspect of the invention provides a multiprocessor, multiuser detection system for detecting user transmitted symbols in CDMA short-code spectrum waveforms. A first processing element generates a matrix (hereinafter, “gamma matrix”) that represents a correlation between a short-code associated with one user and those associated with one or more other users. A set of second processing elements generates, e.g., from the gamma matrix, a matrix (hereinafter, “R-matrix”) that represents cross-correlations among user waveforms based on their amplitudes and time lags. A third processing element produces estimates of the user transmitted symbols as a function of the R-matrix.

BACKGROUND OF THE INVENTION

This application claims the benefit of priority of (i) U.S. ProvisionalApplication Ser. No. 60/275,846 filed Mar. 14, 2001, entitled “ImprovedWireless Communications Systems and Methods”; (ii) U.S. ProvisionalApplication Ser. No. 60/289,600 filed May 7, 2001, entitled “ImprovedWireless Communications Systems and Methods Using Long-Code Multi-UserDetection′” and (iii) U.S. Provisional Application Ser. No. 60/295,060filed Jun. 1, 2001 entitled “Improved Wireless Communications Systemsand Methods for a Communications Computer,” the teachings all of whichare incorporated herein by reference.

The invention pertains to wireless communications and, moreparticularly, by way of example, to methods and apparatus providingmultiple user detection for use in code division multiple access (CDMA)communications. The invention has application, by way of non-limitingexample, in improving the capacity of cellular phone base stations.

Code-division multiple access (CDMA) is used increasingly in wirelesscommunications. It is a form of multiplexing communications, e.g.,between cellular phones and base stations, based on distinct digitalcodes in the communication signals. This can be contrasted with otherwireless protocols, such as frequency-division multiple access andtime-division multiple access, in which multiplexing is based on the useof orthogonal frequency bands and orthogonal time-slots, respectively.

A limiting factor in CDMA communication and, particularly, in so-calleddirect sequence CDMA (DS-CDMA), is interference—both that wrought onindividual transmissions by buildings and other “environmental” factors,as well that between multiple simultaneous communications, e.g.,multiple cellular phone users in the same geographic area using theirphones at the same time. The latter is referred to as multiple accessinterference (MAI). Along with environmental interference, it has effectof limiting the capacity of cellular phone base stations, drivingservice quality below acceptable levels when there are too many users.

A technique known as multi-user detection (MUD) is intended to reducemultiple access interference and, as a consequence, increases basestation capacity. It can reduce interference not only between multipletransmissions of like strength, but also that caused by users so closeto the base station as to otherwise overpower signals from other users(the so-called near/far problem). MUD generally functions on theprinciple that signals from multiple simultaneous users can be jointlyused to improve detection of the signal from any single user. Many formsof MUD are discussed in the literature; surveys are provided in Moshavi,“Multi-User Detection for DS-CDMA Systems,” IEEE Communications Magazine(October, 1996) and Duel-Hallen et al, “Multiuser Detection for CDMASystems,” IEEE Personal Communications (April 1995). Though a promisingsolution to increasing the capacity of cellular phone base stations, MUDtechniques are typically so computationally intensive as to limitpractical application.

An object of this invention is to provide improved methods and apparatusfor wireless communications. A related object is to provide such methodsand apparatus for multi-user detection or interference cancellation incode-division multiple access communications.

A further related object is to provide such methods and apparatus asprovide improved short-code and/or long-code CDMA communications.

A further object of the invention is to provide such methods andapparatus as can be cost-effectively implemented and as require minimalchanges in existing wireless communications infrastructure.

A still further object of the invention is to provide methods andapparatus for executing multi-user detection and related algorithms inreal-time.

A still further object of the invention is to provide such methods andapparatus as manage faults for high-availability.

SUMMARY OF THE INVENTION

The foregoing and other objects are among those attained by theinvention which provides methods and apparatus for multiple userdetection (MUD) processing. These have application, for example, inimproving the capacity CDMA and other wireless base stations

Wireless Communications Systems and Methods for Multiple Processor BasedMultiple User Detection

One aspect of the invention provides a multiuser communications devicefor detecting user transmitted symbols in CDMA short-code spreadspectrum waveforms. A first processing element generates a matrix(hereinafter, “gamma matrix”) that represents a correlation between ashort-code associated with one user and those associated with one ormore other users. A set of second processing elements generates, e.g.,from the gamma matrix, a matrix (hereinafter, “R-matrix”) thatrepresents cross-correlations among user waveforms based on theiramplitudes and time lags. A third processing element produces estimatesof the user transmitted symbols as a function of the R-matrix.

In related aspects, the invention provides a multiuser communicationsdevice in which a host controller performs a “partitioning function,”assigning to each second processing element within the aforementionedset a portion of the R-matrix to generate. This partitioning can be afunction of the number of users and the number of processing elementsavailable in the set. According to related aspects of the invention, asusers are added or removed from the spread spectrum system, the hostcontroller performs further partitioning, assigning each secondprocessing element within the set a new portion of the R-matrix togenerate.

Further related aspects of the invention provide a multiusercommunications device as described above in which the host controller iscoupled to the processing elements by way of a multi-port data switch.Still further related aspects of the invention provide such a device inwhich the first processing element transfers the gamma-matrix to the setof second processing elements via a memory element.

Similarly, the set of second processing elements place the respectiveportions of the R-matrix in memory accessible to the third processingelement via the data switch. Further related aspects of the inventionprovide devices as described above in which the host controller effectsdata flow synchronization between the first processing element and theset of second processing elements, as well as between the set of secondprocessing elements and the third processing element.

Wireless Communications Systems and Methods for Contiguously AddressableMemory Enabled Multiple Processor Based Multiple User Detection

Another aspect of the invention provides a multiuser communicationsdevice for detecting user transmitted symbols in CDMA short-code spreadspectrum waveforms in which a set of first processing elements generatesa matrix (hereinafter the “R-matrix”) that represents cross-correlationsamong user waveforms based on their amplitudes and time lags. The firstprocessing elements store that matrix to contiguous locations of anassociated memory.

Further aspects of the invention provide a device as described above inwhich a second processing element, which accesses the contiguouslystored R-matrix, generates estimates of the user transmitted symbols.

Still further aspects of the invention provide such a device in which athird processing element generates a further matrix (hereinafter,“gamma-matrix”) that represents a correlation between a CDMA short-codeassociated with one user and those associated with one or more otherusers; this gamma-matrix used by the set of first processing elements ingenerating the R-matrix. In related aspects, the invention provides sucha device in which the third processing element stores the gamma-matrixto contiguous locations of a further memory.

In other aspects, the invention provides a multiuser device as describedabove in which a host controller performs a “partitioning function” ofthe type described above that assigning to each processing elementwithin the set a portion of the R-matrix to generate. Still furtheraspects provide such a device in which the host controller is coupled tothe processing elements by way of a multi-port data switch.

Other aspects of the invention provide such a device in which the thirdprocessing element transfers the gamma-matrix to the set of firstprocessing elements via a memory element.

Further aspects of the invention provide a multiuser communicationsdevice as described above with a direct memory access (DMA) engine thatplaces elements of the R-matrix into the aforementioned contiguousmemory locations.

Further aspects of the invention provide methods for operating amultiuser communications device paralleling the operations describedabove.

Wireless Communications Systems and Methods for Cache Enabled MultipleProcessor Based Multiple User Detection

Other aspects of the invention provide a multiuser communications devicethat makes novel use of cache and random access memory for detectinguser transmitted symbols in CDMA short-code spectrum waveforms.According to one such aspect, there is provided a processing elementhaving a cache memory and a random access memory. A host controllerplaces in the cache memory data representative of characteristics of theuser waveforms. The processing element generates a matrix as a functionof the data stored in the cache, and stores the matrix in either thecache or the random access memory.

Further aspects of the invention provide a device as described above inwhich the host controller stores in cache data representative of theuser waveforms short-code sequences. The processing element generatesthe matrix as a function of that data, and stores the matrix in randomaccess memory.

Still further aspects of the invention provide such a device in whichthe host controller stores in cache data representative of a correlationof time-lags between the user waveforms and data representative of acorrelation of complex amplitudes of the user waveforms. The hostcontroller further stores in random access memory data representing acorrelation of short-code sequences for the users waveforms. Theprocessing element generates the matrix as a function of the data andstores that matrix in RAM.

Further aspects of the invention provide a device as described above inwhich a host controller stores in cache an attribute representative of auser waveform, and stores in random access memory an attributesrepresenting a cross-correlation among user waveforms based on time-lagsand complex amplitudes. The processing element generates estimates ofuser transmitted symbols and stores those symbols in random accessmemory.

Other aspects of the invention provide such a device in which the hostcontroller transmits the matrix stored in the cache or random accessmemory of a processing element to the cache or random access memory of afurther processing element.

Further aspects of the invention provide a multiuser communicationsdevice as described above with a multi-port data switch coupled to ashort-code waveform receiver system and also coupled to a hostcontroller. The host controller routes data generated by the receiversystem to the processing element via the data switch.

Further aspects of the invention provide methods for operating amultiuser communications device paralleling the operations describedabove.

Wireless Communications Systems and Methods for Nonvolatile Storage OfOperating Parameters for Multiple Processor Based Multiple UserDetection

Another aspect of the invention provides a multiuser communicationsdevice for detecting user transmitted symbols in CDMA short-codespectrum waveforms in which fault and configuration information isstored to a nonvolatile memory. A processing element, e.g. that performssymbol detection, is coupled with random access and nonvolatilememories. A fault monitor periodically polls the processing element todetermine its operational status. If the processing element isnon-operational, the fault monitor stores information includingconfiguration and fault records, as well at least a portion of data fromthe processing element's RAM, into the nonvolatile memory.

According to further aspects according to the invention, followingdetection of the non-operational status, the fault monitor sends to ahost controller a reset-request interrupt together with the informationstored in the nonvolatile RAM. In turn, the host controller selectivelyissues a reset command to the processing element. In related aspects,the processing element resets in response to the reset command andtransfers (or copies) the data from the nonvolatile memory into the RAM,and therefrom continues processing the data in the normal course.

Further aspects of the invention provide a device as described above inwhich the processing element periodically signals the fault monitor and,in response, the fault monitor polls the processing element. If thefault monitor does not receive such signaling within a specified timeperiod, it sets the operational status of the processing element tonon-operational.

According to a related aspect of the invention, the fault monitor placesthe processing elements in a non-operational status while performing areset. The fault monitor waits a time period to allow for normalresetting and subsequently polls the processor to determine itsoperational status.

Still further aspects of the invention provide a device as describedabove in which there are a plurality of processing elements, each with arespective fault monitor.

Yet still further related aspects of the invention provide for the faultmonitoring a data bus coupled with the processing element.

Further aspects of the invention provide methods for operating amultiuser communications device paralleling the operations describedabove.

Wireless Communications Systems and Methods for Multiple OperatingSystem Multiple User Defection

Another aspect of the invention provides a multiuser communicationsdevice for detecting user transmitted symbols in CDMA short-codespectrum waveforms in which a first process operating under a firstoperating system executes a first set of communication tasks fordetecting the user transmitted symbols and a second process operatingunder a second operating system—that differs from the first operatingsystem—executes a second set of tasks for like purpose. A protocoltranslator translates communications between the processes. According toone aspect of the invention, the first process generates instructionsthat determine how the translator performs such translation.

According to another aspect of the invention, the first process sends aset of instructions to the second process via the protocol translator.Those instructions define the set of tasks executed by the secondprocess.

In a related aspect of the invention, the first process sends to thesecond process instructions for generating a matrix. That can be, forexample, a matrix representing any of a correlation of short-codesequences for the user waveforms, a cross-correlation of the userwaveforms based on time-lags and complex amplitudes, and estimates ofuser transmitted symbols embedded in the user waveforms.

Further aspects of the invention provide a device as described above inwhich the first process configures the second process, e.g., via datasent through the protocol translator. This can include, for example,sending a configuration map that defines where a matrix (or portionthereof) generated by the second process is stored or otherwisedirected.

Still further aspects of the invention provide a device as describedabove in which the first process is coupled to a plurality of secondprocesses via the protocol translator. Each of the latter processes canbe configured and programmed by the first process to generate arespective portion of a common matrix, e.g., of the type describedabove. Further aspects of the invention provide methods for operating amultiuser communications device paralleling the operations describedabove.

Wireless Communications Systems and Methods for Direct Memory Access andBuffering Of Digital Signals for Multiple User Detection

Another aspect of the invention provides a multiuser communicationsdevice for detecting user transmitted symbols in CDMA short-codespectrum waveforms in which a programmable logic device (hereinafter“PLD”) enables direct memory access of data stored in a digital signalprocessor (hereinafter “DSP”). The DSP has a memory coupled with a DMAcontroller that is programmed via a host port. The PLD programs the DMAcontroller via the host port to allow a buffer direct access to thememory.

In a related aspect according to the invention, the PLD programs the DMAcontroller to provide non-fragmented block mode data transfers to thebuffer. From the buffer, the PLD moves the blocks to a data switch thatis coupled to processing devices. In a further related aspects accordingto the invention, the PLD programs the DMA controller to providefragmented block mode data transfers utilizing a protocol. The PLDprovides the protocol which fragments and unfragments the blocks priorto moving them to the data switch.

In further aspects provided by a device as described above, the PLD isimplemented as a field programmable gate array that is programmed by ahost controller coupled with the data switch. In a related aspect, thePLD is implemented as a application specific integrated circuit which isprogrammed during manufacture. In still aspects, a device as describedabove provides for a buffer implemented as a set of registers, or asdual-ported random access memory.

Further aspects of the invention provide methods for operating amultiuser communications device paralleling the operations describedabove.

Improved Wireless Communications Systems and Methods for Short-codeMultiple User Detection

Still further aspects of the invention provide methods for processingshort code spread spectrum waveforms transmitted by one or more usersincluding the step of generating a matrix indicative of crosscorrelations among the waveforms as a composition of (i) a firstcomponent that represents correlations among time lags and short codesassociated with the waveforms transmitted by the users, and (ii) asecond component that represents correlations among multipath signalamplitudes associated with the waveforms transmitted by the users. Themethod further includes generating detection statistics corresponding tothe symbols as a function of the correlation matrix, and generatingestimates of the symbols based on those detection statistics.

Related aspects of the invention provided methods as described above inwhich the first component is updated on a time scale that iscommensurate with a rate of change of the time lags associated with thetransmitted waveforms, and the second component is updated on adifferent time scale, i.e., one that is commensurate with a rate ofchange of the multipath amplitudes associated with these waveforms. Inmany embodiments, the updating of the second component, necessitated asa result of change in the multipath amplitudes, is executed on a shortertime scale than that of updating the first component.

Other aspects of the invention provide methods as described above inwhich the first component of the cross-correlation matrix is generatedas a composition of a first matrix component that is indicative ofcorrelations among the short codes associated with the respective users,and a second matrix component that is indicative of the waveformstransmitted by the users and the time lags associated with thosewaveforms.

In a related aspect, the invention provides methods as above in whichthe first matrix component is updated upon addition or removal of a userto the spread spectrum system. This first matrix component (referred tobelow as Γ-matrix) can be computed as a convolution of the short codesequence associated with each user with the short codes of other users.

According to further aspects of the invention, elements of the Γ-matrixare computed in accord with the relation:

${\Gamma_{l\; k}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N - 1}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}$

-   -   wherein    -   c_(l) ^(*)[n] represents the complex conjugate of a short code        sequence associated with the l^(th) user,    -   c_(k)[n−m] represents a short code sequence associated with the        k^(th) user,    -   N represents a length of the short code sequence, and    -   N_(l) represent a number of non-zero length of the short code        sequence.

In further aspects, the invention provides a method as described abovein which the first component of the cross-correlation matrix (referredto below as the C matrix) is obtained as a function of theaforementioned Γ-matrix in accord with the relation:

${C_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack} = {\sum\limits_{m}{{g\left\lbrack {{m\; N_{c}} + \tau} \right\rbrack} \cdot {\Gamma_{l\; k}\lbrack m\rbrack}}}$

-   -   wherein    -   g is a pulse shape vector,    -   Nc is the number of samples per chip,    -   τ is a time lag, and    -   Γ represents the Γ matrix, e.g., defined above.

In a related aspect, the cross-correlation matrix (referred to below asthe R-matrix) can be generated as a function of the C matrix in accordwith the relation:

${r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {{\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {{\hat{a}}_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot {C_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack}}} \right\}}}} = {R\; e\left\{ {a_{l}^{H} \cdot {C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k}} \right\}}}$

-   -   wherein    -   â_(lq) ^(*) is an estimate of a_(lq) ^(*), the complex conjugate        of one multipath amplitude component of the l^(th) user,    -   a_(kq) is one multipath amplitude component associated with the        k^(th) user, and    -   C denotes the C matrix, e.g., as defined above.

In further aspects, the invention provides methods as described above inwhich the detection statistics are obtained as a function of thecross-correlation matrix (e.g., the R-matrix) in accord with therelation:

${y_{l}\lbrack m\rbrack} = {{{r_{l\; l}\lbrack 0\rbrack}{b_{l}\lbrack m\rbrack}} + {\sum\limits_{k = 1}^{K_{y}}{{r_{l\; k}\left\lbrack {- 1} \right\rbrack}{b_{k}\left\lbrack {m + 1} \right\rbrack}}} + {\sum\limits_{k = 1}^{K_{y}}{\left\lbrack {{r_{l\; k}\lbrack 0\rbrack} - {{r_{l\; l}\lbrack 0\rbrack}\delta_{l\; k}}} \right\rbrack{b_{k}\lbrack m\rbrack}}} + {\sum\limits_{k = 1}^{K_{y}}{{r_{l\; k}\lbrack 1\rbrack}{b_{k}\left\lbrack {m - 1} \right\rbrack}}} + {\eta_{l}\lbrack m\rbrack}}$

-   -   wherein    -   y_(l)[m] represents a detection statistic corresponding to        m^(th) symbol transmitted by the l^(th) user,    -   r_(ll)[0]b_(l)[m] represents a signal of interest, and    -   remaining terms of the relation represent Multiple Access        Interference (MAI) and noise.

In a related aspect, the invention provides methods as described abovein which estimates of the symbols transmitted by the users and encodedin the short code spread spectrum waveforms are obtained based on thecomputed detection statistics by utilizing, for example, a multi-stagedecision-feedback interference cancellation (MDFIC) method. Such amethod can provides estimates of the symbols, for example, in accordwith the relation:

${{\hat{b}}_{l}\lbrack m\rbrack} = {s\; i\; g\; n\left\{ {{y_{l}\lbrack m\rbrack} - {\sum\limits_{k = 1}^{K_{y}}{{r_{l\; k}\left\lbrack {- 1} \right\rbrack}{{\hat{b}}_{k}\left\lbrack {m + 1} \right\rbrack}}} - {\sum\limits_{k = 1}^{K_{y}}{\left\lbrack {{r_{l\; k}\lbrack 0\rbrack} - {{r_{l\; l}\lbrack 0\rbrack}\delta_{i\; k}}} \right\rbrack{{\hat{b}}_{k}\lbrack m\rbrack}}} - {\sum\limits_{k = 1}^{K_{y}}{{r_{l\; k}\lbrack 1\rbrack}{{\hat{b}}_{k}\left\lbrack {m + 1} \right\rbrack}}}} \right\}}$

-   -   wherein    -   {circumflex over (b)}_(l)[m] represents an estimate of the        m^(th) symbol transmitted by the l^(th) user.

Further aspects of the invention provide logic carrying out operationsparalleling the methods described above.

Load Balancing Computational Methods in a Short-Code Spread-SpectrumCommunications System

In further aspects, the invention provides methods for computing thecross-correlation matrix described above by distributing among aplurality of logic units parallel tasks—each for computing a portion ofthe matrix. The distribution of tasks is preferably accomplished bypartitioning the computation of the matrix such that the computationalload is distributed substantially equally among the logic units.

In a related aspect, a metric is defined for each partition in accordwith the relation below. The metric is utilized as a measure of thecomputational load associated with each logic unit to ensure that thecomputational load is distributed substantially equally among the logicunits:B _(i) =A _(i) −A _(i)−1

-   -   wherein        -   A_(i) represents an area of a portion of the            cross-correlation matrix corresponding to the i^(th)            partition, and        -   i represents an index corresponding to the number of logic            units over which the computation is distributed.

In another aspect, the invention provides methods as described above inwhich the cross-correlation matrix is represented as a composition of arectangular component and a triangular component. Each area, representedby A_(i) in the relation above, includes a first portion correspondingto the rectangular component and a second portion corresponding to thetriangular component.

Further aspects of the invention provide logic carrying out operationsparalleling the methods described above.

Hardware and Software for Performing Computations in a Short-CodeSpread-Spectrum Communications System

In other aspects, the invention provides an apparatus for efficientlycomputing a Γ-matrix as described above, e.g., in hardware. The systemincludes two registers, one associated with each of l^(th) and k^(th)users. The registers hold elements of the short code sequencesassociated with the respective user such that alignment of the shortcode sequence loaded in one register can be shifted relative to that ofthe other register by m elements. Associated with each of the foregoingregisters is one additional register storing mask sequences. Eachelement in those sequences is zero if a corresponding element of theshort code sequence of the associated register is zero and, otherwise,is non-zero. The mask sequences loaded in these further registers areshifted relative to the other by m elements. A logic performs anarithmetic operation on the short code and mask sequences to generate,for m^(th) transmitted symbol, the (l, k) element of the Γ-matrix, i.e.,Γ_(lk)[m]

In a related aspect, the invention provides an apparatus as describedabove in which the arithmetic operation performed by the logic unitincludes, for any two aligned elements of the short code sequences ofthe l^(th) and k^(th) user and the corresponding elements of the masksequences, (i) an XOR operation between the short code elements, (ii) anAND operation between the mask elements, (iii) an AND operation betweenresults of the step (i) and step (ii). The result of step (iii) is amultiplier for the aligned elements, which the logic sums in order togenerate the (l, k) element of the Γ-matrix.

Further aspects of the invention provide methods paralleling theoperations described above.

Improved Computational Methods for Use in a Short-Code Spread-SpectrumCommunications System

In still further aspects, the invention provides improved computationalmethods for calculating the aforesaid cross-correlation matrix byutilizing a symmetry property. Methods according to this aspect includecomputing a first one of two matrices that are related by a symmetryproperty, and calculating a second one of the two matrices as a functionof the first component through application of the symmetry property.

According to related aspects of the invention, the symmetry property isdefined in accord with the relation:R _(lk)(m)=ξR _(k,l)(−m).

-   -   wherein    -   R_(lk)(m) and R_(kl)(m) refer to (l, K) and (k, l) elements of        the cross-correlation matrix, respectively.

Further aspects of the invention provide methods as described above inwhich calculation of the cross-correlation matrix further includesdetermining a C matrix that represents correlations among time lags andshort codes associated with the waveforms transmitted by the users, andan R-matrix that represents correlations among multipath signalamplitudes associated with the waveforms transmitted by the users. Inrelated aspects the step of determining the C matrix includes generatinga first of two C-matrix components related by a symmetry property. Asecond of the components is then generated by applying the symmetryproperty.

Related aspects of the invention provide a method as described aboveincluding the step of generating the Γ-matrix in accord with therelation:

${\Gamma_{l\; k}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N - 1}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}$

-   -   wherein    -   c_(l) ^(*)[n] represents complex conjugate of the short code        sequence associated with the lth user,    -   c_(λ)[n−m] represents the short code sequence associated with        kth user,    -   N represents the length of the code, and    -   N_(l) represent the number of non-zero length of the code.

Further aspects of the invention provide logic carrying out operationsparalleling the methods described above.

Wireless Communications Systems and Methods for Virtual User BasedMultiple User Detection Utilizing Vector Processor Generated MappedCross-Correlation Matrices

Still further aspects of the invention provide methods for detectingsymbols encoded in physical user waveforms, e.g., those attributable tocellular phones, modems and other CDMA signal sources, by decomposingeach of those waveforms into one or more respective virtual userwaveforms. Each waveform of this latter type represents at least aportion of a symbol encoded in the respective physical user waveformsand, for example, can be deemed to “transmit” a single bit per symbolperiod. Methods according to this aspect of the invention determinecross-correlations among the virtual user waveforms as a function of oneof more characteristics of the respective physical user waveforms. Fromthose cross-correlations, the methods generate estimates of the symbolsencoded in the physical user waveforms.

Related aspects of the invention provide methods as described above inwhich a physical user waveforms is decomposed into a virtual userwaveform that represents one or more respective control or data bits ofa symbol encoded in the respective physical user waveform.

Other related aspects provide for generating the cross-correlations inthe form of a first matrix, e.g., an R-matrix for the virtual userwaveforms. That matrix can, according to still further related aspectsof the invention, be used to generate a second matrix representingcross-correlations of the physical user waveforms. This second matrix isgenerated, in part, as a function of a vector indicating the mapping ofvirtual user waveforms to physical user waveforms.

Further aspects of the invention provide a system for detecting symbolsencoded in physical user waveforms that has multiple processors, e.g.,each with an associated vector processor, that operates in accord withthe foregoing methods to generate estimates of the symbols encoded inthe physical user waveforms.

Still other aspects of the invention provide a system for detecting usertransmitted symbols encoded in short-code spread spectrum waveforms thatgenerates cross-correlations among the waveforms as a function ofblock-floating integer representations of one or more characteristics ofthose waveforms. Such a system, according to related aspects of theinvention, utilizes a central processing unit to form floating-pointrepresentations of virtual user waveform characteristics intoblock-floating integer representations. A vector processor, according tofurther related aspects, generates the cross-correlations from thelatter representations. The central processing unit can “reformat” theresulting block-floating point matrix into floating-point format, e.g.,for use in generating symbol estimates.

Still further aspects of the invention provide methods and apparatusemploying any and all combinations of the foregoing. These and otheraspects of the invention, which includes combinations of the foregoing,are evident in the illustrations and in the text that follows.

BRIEF DESCRIPTION OF THE ILLUSTRATED EMBODIMENT

A more complete understanding of the invention may be attained byreference to the drawings, in which:

FIG. 1 is a block diagram of components of a wireless base-stationutilizing a multiuser detection apparatus according to the invention;

FIG. 2 is a block diagram of components of a multiple user detectionprocessing card according to the invention;

FIG. 3 is a more detailed view of the processing board of FIG. 2;

FIG. 4 depicts a majority-voter sub-system in a system according to theinvention;

FIG. 5 is a block diagram of an integrated direct memory access (DMA)engine of the type used in a system according to the invention;

FIGS. 6 and 7 depict power on/off curves for the processor board in asystem according to the invention;

FIG. 8 are an operational overview of functionality within the hostprocessor and multiple compute nodes in a system according to theinvention;

FIG. 9 is a block diagram of an external digital signal processorapparatus used to supply digital signals to the processor board in asystem according to the invention;

FIG. 10 illustrates an example of loading the R matrices on multiplecompute nodes in a system according to the invention;

FIG. 11 depicts a short-code loading implementation with parallelprocessing of the matrices in a system according to the invention;

FIG. 12 depicts a long-code loading implementation utilizing pipelinedprocessing and a triple-iteration of refinement in a system according tothe invention;

FIG. 13 illustrates skewing of multiple user waveforms;

FIG. 14 is a graph illustrating MUD efficiency as a function of uservelocity in units of Km/hr.

FIG. 15 schematically illustrates a method for defining a commoninterval for three short-code streams utilized in a FFT calculation ofthe Γ-matrix;

FIG. 16 schematically illustrates the Γ-matrix elements calculated uponaddition of a new physical user to a system according to the invention;

FIGS. 17, 18 and 19 depict hardware calculation of the Γ-matrix in asystem according to the invention;

FIG. 20 illustrates parallel computation of the R and C matrices in asystem according to the invention;

FIG. 21 depicts a use of a vector processor using integer operands forgenerating a cross-correlation matrix of virtual user waveforms in asystem according to the invention.

DETAILED DESCRIPTION OF THE ILLUSTRATED EMBODIMENT

Code-division multiple access (CDMA) waveforms or signals transmitted,e.g., from a user cellular phone, modem or other CDMA signal source, canbecome distorted by, and undergo amplitude fades and phase shifts due tophenomena such as scattering, diffraction and/or reflection offbuildings and other natural and man-made structures. This includes CDMA,DS/CDMA, IS-95 CDMA, CDMAOne, CDMA2000 1X, CDMA2000 1xEV-DO, WCDMA (orUTMS), and other forms of CDMA, which are collectively referred tohereinafter as CDMA or WCDMA. Often the user or other source(collectively, “user”) is also moving, e.g., in a car or train, addingto the resulting signal distortion by alternately increasing anddecreasing the distances to and numbers of building, structures andother distorting factors between the user and the base station.

In general, because each user signal can be distorted several differentways en route to the base station or other receiver (hereinafter,collectively, “base station”), the signal may be received in severalcomponents, each with a different time lag or phase shift. To maximizedetection of a given user signal across multiple tag lags, a rakereceiver is utilized. Such a receiver is coupled to one or more RFantennas (which serve as a collection point(s) for the time-laggedcomponents) and includes multiple fingers, each designed to detect adifferent multipath component of the user signal. By combining thecomponents, e.g., in power or amplitude, the receiver permits theoriginal waveform to be discerned more readily, e.g., by downstreamelements in the base station and/or communications path.

A base station must typically handle multiple user signals, and detectand differentiate among signals received from multiple simultaneoususers, e.g., multiple cell phone users in the vicinity of the basestation. Detection is typically accomplished through use of multiplerake receivers, one dedicated to each user. This strategy is referred toas single user detection (SUD). Alternately, one larger receiver can beassigned to demodulate the totality of users jointly. This strategy isreferred to as multiple user detection (MUD). Multiple user detectioncan be accomplished through various techniques which aim to discern theindividual user signals and to reduce signal outage probability orbit-error rates (BER) to acceptable levels.

However, the process has heretofore been limited due to computationalcomplexities which can increase exponentially with respect to the numberof simultaneous users. Described below are embodiments that overcomethis, providing, for example, methods for multiple user detectionwherein the computational complexity is linear with respect to thenumber of users and providing, by way of further example, apparatus forimplementing those and other methods that improve the throughput of CDMAand other spread-spectrum receivers. The illustrated embodiments areimplemented in connection with short-code CDMA transmitting and receiverapparatus; however those skilled in the art will appreciate that themethods and apparatus therein may be used in connection with long-codeand other CDMA signalling protocols and receiving apparatus, as well aswith other spread spectrum signalling protocols and receiving apparatus.In these regards and as used herein, the terms long-code and short-codeare used in their conventional sense: the former referring to codes thatexceed one symbol period; the latter, to codes that are a single symbolperiod or less.

FIG. 1 depicts components of a wireless base station 100 of the type inwhich the invention is practiced. The base station 100 includes anantenna array 114, radio frequency/intermediate frequency (RF/IF)analog-to-digital converter (ADC), multi-antenna receivers 110, rakemodems 112, MUD processing logic 118 and symbol rate processing logic120, coupled as shown.

Antenna array 114 and receivers 110 are conventional such devices of thetype used in wireless base stations to receive wideband CDMA(hereinafter “WCDMA”) transmissions from multiple simultaneous users(here, identified by numbers l through K). Each RF/IF receiver (e.g.,110) is coupled to antenna or antennas 114 in the conventional mannerknown in the art, with one RF/IF receiver 110 allocated for each antenna114. Moreover, the antennas are arranged per convention to receivecomponents of the respective user waveforms along different laggedsignal paths discussed above. Though only three antennas 114 and threereceivers 110 are shown, the methods and systems taught herein may beused with any number of such devices, regardless of whether configuredas a base station, a mobile unit or otherwise. Moreover, as noted above,they may be applied in processing other CDMA and wireless communicationssignals.

Each RF/IF receiver 110 routes digital data to each modem 112. Becausethere are multiple antennas, here, Q of them, there are typically Qseparate channel signals communicated to each modem card 112.

Generally, each user generating a WCDMA signal (or other subjectwireless communication signal) received and processed by the basestation is assigned a unique short-code code sequence for purposes ofdifferentiating between the multiple user waveforms received at thebasestation, and each user is assigned a unique rake modem 112 forpurposes of demodulating the user's received signal. Each modem 112 maybe independent, or may share resources from a pool. The rake modems 112process the received signal components along fingers, with each receiverdiscerning the signals associated with that receiver's respective usercodes. The received signal components are denoted here as r_(kq)[t]denoting the channel signal (or waveform) from the k^(th) user from theq^(th) antenna, or r_(k)[t] denoting all channel signals (or waveforms)originating from the k^(th) user, in which case r_(k)[t] is understoodto be a column vector with one element for each of the Q antennas. Themodems 112 process the received signals r_(k)[t] to generate detectionstatistics y_(k) ⁽⁰⁾[m] for the k^(th) user for the mth symbol period.To this end, the modems 122 can, for example, combine the componentsr_(kq)[t] by power, amplitude or otherwise, in the conventional mannerto generate the respective detection statistics y_(k) ⁽⁰⁾[m]. In thecourse of such processing, each modem 112 determines the amplitude(denoted herein as α) of and time lag (denoted herein as τ) between themultiple components of the respective user channel. The modems 112 canbe constructed and operated in the conventional manner known in the art,optionally, as modified in accord with the teachings of some of theembodiments below.

The modems 112 route their respective user detection statistics y_(k)⁽⁰⁾[m], as well as the amplitudes and time lags, to common userdetection (MUD) 118 logic constructed and operated as described in thesections that follow. The MUD logic 118 processes the received signalsfrom each modem 112 to generate a refined output, y_(k) ⁽¹⁾[m], or moregenerally, y_(k) ^((n))[m], where n is an index reflecting the number oftimes the detection statistics are iteratively or regenerativelyprocessed by the logic 118. Thus, whereas the detection statisticproduced by the modems is denoted as y_(k) ⁽⁰⁾[m] indicating that therehas been no refinement, those generated by processing the y_(k) ⁽¹⁾[m]detection statistics with logic 118 are denoted y_(k) ⁽¹⁾[m], thosegenerated by processing the y_(k) ⁽¹⁾[m] detection statistics with logic118 are denoted y_(k) ⁽²⁾[m], and so forth. Further waveforms used andgenerated by logic 118 are similarly denoted, e.g., r^((n))[t].

Though discussed below are embodiments in which the logic 118 isutilized only once, i.e., to generate y_(k) ^((l))[m] from y_(k) ⁽⁰⁾[m],other embodiments may employ that logic 118 multiple times to generatestill more refined detection statistics, e.g., for wirelesscommunications applications requiring lower bit error rates (BER). Forexample, in some implementations, a single logic stage 118 is used forvoice applications, whereas two or more logic stages are used for dataapplications. Where multiple stages are employed, each may be carriedout using the same hardware device (e.g., processor, co-processor orfield programmable gate array) or with a successive series of suchdevices.

The refined user detection statistics, e.g., y_(k) ⁽¹⁾[m] or moregenerally y_(k) ^((n))[m], are communicated by the MUD process 118 to asymbol process 120. This determines the digital information containedwithin the detection statistics, and processes (or otherwise directs)that information according to the type of user class for which the userbelongs, e.g., voice or data user, all in the conventional manner.

Though the discussion herein focuses on use of MUD logic 118 in awireless base station, those skilled in the art will appreciate that theteachings hereof are equally applicable to MUD detection in any otherCDMA signal processing environment such as, by way of nonlimitingexample, cellular phones and modems. For convenience, such cellular basestations other environments are referred to herein as “base stations.”Multiple User Detection Processing Board

FIG. 2 depicts a multiple user detection (MUD) processing card accordingto the invention. The illustrated processing card 118 includes a hostprocessor 202, an interface block 204, parallel processors 208, a frontpanel device 210, and a multi-channel cross-over device 206 (hereinafter“Crossbar”). Although these components are shown as separate entities,one skilled in the art can appreciate that different configurations arepossible within the spirit of the invention. For example, the hostprocessor 202 and the interface block 204 can be integrated into asingle assemble, or multiple assemblies.

The processing card 118 processes waveform and waveform componentsreceived by a base station, e.g., from a modem card 112 or receiver 110contained within the base station, or otherwise coupled with the basestation. The waveform typically includes CDMA waveforms, however theprocessing card 118 can also be configured for other protocols, such asTDMA and other multiple user communication techniques. The processingcard 118 performs multiple user detection (MUD) on the waveform data,and generates a user signal corresponding to each user, with includesless interference than within the received signals.

The illustrated processing card 118 is a single board assembly and ismanufactured to couple (e.g., electrically and physically mate) with aconventional base station (e.g., a modem card 112, receiver 110 or othercomponent). The board assembly illustrated conforms to a 3/4 form factormodem payload card of the type available in the marketplace. Theprocessor card 118 is designed for retrofitting into existing basestations or for design into new station equipment. In other embodiments,the processing card can be either single or multiple assemblies.

The host processor 202 routes data from the interface block 204 to andamong the parallel processors 208, as well as performs fault monitoringand automated resets, data transfer, and processor loading of theparallel processors 208. The host processor 202 also processes outputreceived from the parallel processors 208, and communicates theprocessed output to the interface block 204 for subsequent return to thebase station.

The parallel processors 202 process waveforms and waveform componentsrouted from the host processor 206. Typically, the parallel processors202 process the waveform components, and communicate the processed databack to the host processor 202 for further processing and subsequenttransmission to the base station, however, the intermediate processedwaveforms can be communicated to other parallel processors or directlyto the base station.

The crossbar 206 is a communication switch which routes messages betweenmultiple devices. It allows multiple connection data ports to beconnection with other data ports. In the illustrated embodiment, thecrossbar 206 provides eight ports, where a port can be “connected” toany other port (or to multiple ports) to provide communication betweenthose two (or indeed, multiple) ports. Here, the crossbar 206 is aRACEway™ switch of the type commercially available from the assigneehereof. In other embodiments, other switching elements, whetherutilizing the RACEway™ protocol or otherwise, may be used, e.g., PCI,I2C and so on. Indeed, in some embodiments, the components communicatealong a common bus and/or are distributed via over a network.

A front panel 210 is used to monitor the processor card and can be usedto apply software patches, as well as perform other maintenanceoperations. Additionally, the front panel 210 can be used to monitorfault status and interface connections through a series of LEDindicators, or other indicators. Illustrated front panel interfaces withthe board via the RACEway™ switch and protocol, though other interfacetechniques may be used as well.

FIG. 3 depicts further details of the processor card of FIG. 2. Theillustrated processor card includes a host processor 202 incommunication with an interface block 205 and a set of parallelprocessors 208 (hereinafter “compute elements”) as described above, aswell as a crossbar 206 and a front panel 210. Further, a powerstatus/control device 240 is assembled on the processor card 118.However, in other embodiments, the power status/control device 240 canbe within the base station or elsewhere.

The host processor 202 includes a host controller 203 with an integratedprocessor containing a peripheral logic block and a 32-bit processorcore. The host controller 203 is coupled with various memory devices205, a real time clock 206, and a protocol translator 208. In theillustrated embodiment, the host controller 203 can be a MotorolaPowerPC 8240 commercially available, but it will be appreciated by oneskilled in the art that other integrated processors (or evennon-integrated processors) can be used which satisfy the requirementsherein.

The host controller 203 controls data movement within the processor card118 and between the processor card and the base station. It controls thecrossbar device 206 by assigning the connection between connectionports. Further, the host controller 203 applies functionality to theoutput generated by the parallel processors 208. The host controller 203includes a monitor/watchdog sub-system which monitors the perform ace ofthe various components within the processor card, and can issue resetsto the components. In some embodiments, these functions can be provided(or otherwise assisted) by application specific integrated circuits orfield programmable gate arrays.

The host controller 203 integrates a PCI bus 211 a, 211 b for datamovement with the memory devices 205 and the interface block 205, aswell as other components. The PCI bus 211 a, 211 b is capable of 32-bitor 64-bit data transfers operating at 33 MHz, or alternatively 66 MHzspeeds, and supports access to PCI memory address spaces using either(or both) little and/or big endian protocols.

Memory devices used by the host controller 203 include HA Registers 212,synchronous dynamic random access memory (SDRAM) 214, Flash memory 216,and Non-Volatile Ram (NVRAM) 218. As will be evident below, each type ofmemory is used for differing purposes.

The HA registers 212 store operating status (e.g., faults) for theparallel processors 208, the power status/control device 240, and othercomponents. A fault monitoring sub-system “watchdog” writes bothsoftware and hardware status into the HA registers 212, from which thehost controller 203 monitors the registers 212 to determine theoperational status of the components. The HA registers 212 are mappedinto banked memory locations, and are thereby addressable as directaccess registers. In some embodiments, the HA registers 212 can beintegrated with the host controller 203 and still perform the samefunction.

The SDRAM 214 stores temporary application and data. In the illustratedembodiment, there is 64 Kbytes of SDRAM 214 available to supporttransient data, e.g., intermediary results from processing and temporarydata values. The SDRAM 214 is designed to be directly accessed by thehost controller 203 allowing for fast DMA transfers.

The flash memory 216 includes two Intel StrataFlash devices, althoughequivalent memory devices are commercially available. It stores datarelated to component performance data, and intermediate data which canbe used to continue operation after resets are issued. The flash memoryis blocked at 8 Kbyte boundaries, but in other embodiments, the blocksize can vary depending on the addressing capabilities of the hostcontroller 203 and method of communication with the memory devices.Further, because flash memory requires no power source to retainprogrammed memory data, its data can be used for diagnostic purposeseven in the event of power-failures.

NVRAM is, to an extent, reserved for fault record data and configurationinformation. Data stored within the NVRAM 218, together with the flashmemory 216 is sufficient to reproduce the data within the SDRAM 218 uponsystem (or board level, or even component level) reset. If a componentis reset during operation, the host controller 203 can continueoperation without the necessity of receiving additional information fromthe base station via the data stored in the NVRAM. The NVRAM 218 iscoupled to the host controller 203 via a buffer which converts thevoltage of the PCI bus 211 a from 3.3 v to 5 v, as required by the NVRAM218, however this conversion is not necessary in other embodiments withdifferent memory configurations.

The interface block 205 includes a PCI bridge 222 in communication withan Ethernet interface 224 and a modem connection 226. The PCI bridge 222translates data received from the PCI bus 211 b into a protocolrecognized by the base station modem card 112. Here, the modemconnection 226 operates with a 32-bit interface operating at 66 MHz,however, in other embodiments the modem can operate with differentcharacteristics. The Ethernet connection 224 can operate at either 10Mbytes/Sec or 100 Mbytcs/Sec, and is therefore suited for most Ethernetdevices. Those skilled in the art can appreciate that these interfacedevices can be interchanged with other interface devices (e.g., LAN,WAN, SCSI and the like).

The real-time clock 206 supplies timing for the host controller 203 andthe parallel processors 208, and thus, synchronizes data movement withinthe processing card. It is coupled with the host controller 203 via anintegrated I2C bus (as established by Phillips Corporation, although inother embodiments the clock can be connected via other electricalcoupling). The real-time clock 206 is implemented as a CMOS device forlow power consumption. The clock generates signals which control addressand data transfers within the host controller 203 and the multipleprocessors 208.

A protocol converter 208 (hereinafter “PXB”) converts PCI protocol usedby the host controller 203 to RACEway™ protocol used by the parallelprocessors 208 and front panel 210. The PXB 208 contains a fieldprogrammable gate array ( “FPGA”) and EEPROM which can be programmedfrom the PCI bus 211 b. In some embodiments, the PXB 208 is programmedduring manufacture of the processing card 118 to contain configurationinformation for the related protocols and/or components with which itcommunicates. In other embodiments, the PXB 208 can use other protocolsas necessary to communicate with the multiple processors 208. Of course,if the host controller 203 and the multiple processors 208 use the sameprotocol, there is no protocol conversion necessary and therefore thePXB is not required.

The multiple-port communication device 206 (hereinafter “crossbar”)provides communication between all processing and input/output elementson the processing card 118. In the illustrated embodiment, the crossbar206 is an EEPROM device which can be read and programmed by a RACEway™compatible component (e.g., the front panel 210 or parallel processors208), but it is typically programmed initially during manufacture. Anembedded ASIC device controls the EEPROM programming, and hence, thefunction of the crossbar 206.

The crossbar 206 in the illustrated provides up to three simultaneous266-Mbytes/Sec throughput data paths between elements for a totalthroughput of 798 Mbytes/Sec, however, in other embodiments the actualthroughput varies according to processing speed. Here, two crossbarports (e.g., ports 0 and 1) connect to a bridge FPGA which furtherconnect to the front panel 210. Each of the multiple processors use ancrossbar port (e.g., ports 2, 3, 5, and 6 ), and the interface block 224and host controller 203 share one crossbar port (e.g., port 4 ) via thePXB 206. The number of ports on the crossbar 206 depends on the numberof parallel processors and other components that are in communication.

The multiple processors 208 in the illustrated embodiment include fourcompute elements 220 a–220 d (hereinafter, reference to element 220refers to a general compute element, also referred to herein as a“processing element” or “CE”). Each processing element 220 appliesfunctionality on data, and generates processed date in the form of amatrix, vector, or waveform. The processing elements 220 can alsogenerate scalar intermediate values. Generated data is passed to thehost controller 208, or to other processing elements 220 for furtherprocessing. Further, individual processing elements can be partitionedto operate in series (e.g., as a pipeline) or in parallel with the otherprocessing elements.

A processing element 220 includes a processor 228 coupled with a cache230, a Joint Test Action Group (hereinafter “JTAG”) interface 232 withan integrated programming port, and an application specific integratedcircuit 234 (hereinafter “ASIC”). Further, the ASIC 234 is coupled witha 128 Mbyte SDRAM device 236 and HA Registers 238. The HA Registers arecoupled with 8 Kbytes of NVRAM 244. In the illustrated embodiment thecompute elements 220 are on the same assembly as the host controller203. In other embodiments, the compute nodes 220 can be separate fromthe host controller 203 depending on the physical and electricalcharacteristics of the target base station.

The compute node processors 228 illustrated are Motorola PowerPC 7400,however in other embodiments the processor can be other processordevices. Each processor 228 uses the ASIC 234 to interface with aRACEway™ bus 246. The ASIC 234 provides certain features of a computenode 220, e.g., a DMA engine, mail box interrupts, timers, page mappingregisters, SDRAM interface and the like. In the illustrated embodimentthe ASIC is programmed during manufacture, however, it can also beprogrammed in the field, or even at system reset in other embodiments.

The cache 230 for each compute node 220 stores matrices that areslow-changing or otherwise static in relation to other matrices. Thecache 230 is pipelined, single-cycle deselect, synchronous burst staticrandom access memory, although in other embodiments high-speed RAM orsimilar devices can be used. The cache 230 can be implemented usingvarious devices, e.g., multiple 64 Kbyte devices, multiple 256 Kbytedevices, and so on.

Architecture Pairing of Processing Nodes with NVRAM and Watchdog;Majority Voter

The HA registers 238 store fault status for the software and/or hardwareof the compute element 220. As such, it responds to the watchdog faultmonitor which also monitors the host controller 203 and othercomponents. The NVRAM 244 is, much like the NVRAM coupled with the hostcontroller 203, stores data from which the current state of the computeelement 220 can be recreated should a fault or reset occur. The SDRAM236 is used for intermediate and temporary data storage, and is directlyaddressable from both the ASIC 234 and the processor 228. These memorydevices can be other devices in other embodiments, depending on speedrequirements, throughput and computational complexity of the multipleuser detection algorithms.

NVRAM is also used to store computational variables and data such thatupon reset of the processing element or host controller, execution canbe restarted without the need to refresh the data. Further, the contentsof NVRAM can be used to diagnose fault states and/or conditions, thusaiding to a determination of the cause of fault state.

As noted above, a “watchdog” monitors performance of the processing card118. In the illustrated embodiment, there are five independent“watchdog” monitors on the processing card 118 (e.g., one for the hostcontroller 203 and one each for each compute node 220 a–220 d, and soon). The watchdog also monitors performance of the PCI bus as well asthe RaceWay bus connected with each processing element and the dataswitch. The RACEWay bus includes out-of-band fault management coupledwith the watchdogs.

Each component periodically strobes its watchdog at least every 20 msecbut not faster that 500 microseconds (these timing parameters vary amongembodiments depending on overall throughput of the components and clockspeed). The watchdog is initially strobed approximately two secondsafter the initialization of a board level reset, which allows forstart-up sequencing of the components without cycling erroneous resets.Strobing the watchdog for the processing nodes is accomplished bywriting a zero or a one sequence to a discrete word (e.g., within the HARegister 212) originating within each compute element 220 a–220 d, thehost controller 203, and other components). The watchdog for the hostcontroller 203 is serviced by writing to the memory mapped discretelocation FFF_D027 which is contained within the HA Registers 212.

The watchdog uses five 8-bit status registers within the HA registers212, and additional registers (e.g., HA registers 238) within eachcompute node 220. One register represents the host controller 203status, and the other four represent each compute node 220 a–220 dstatus. Each register has a format as follows:

Bit Name Description 0 CHECKSTOP_OUT Checkstop state of CPU (0 = CPU incheckstop) 1 WDM_FAULT WDM failed (0 = WDM failed, set high after resetand valid service) 2 SOFTWARE_FAULT Software fault detected (Set to 0when a software exception was detected) (R/W local) 3 RESETREQ_IN Wrapstatus of the local CPU's reset request 4 WDM_INIT WDM failed in initial2 second window (0 = WDM failed) 5 Software definable 0 Softwaredefinable 0 6 Software definable 1 Software definable 1 7 Unused Unused

The five registers reflect status information for all processors withinthe processing board 118, and allow the host controller 203 to obtainstatus of each without the need for polling the processor individually(which would degrade performance and throughput). Additionally, the hostcontroller 203 and each compute node processor 228 has a fault controlregister which contains fault data according to the following format:

Bit Name Description 0 RESETREQ_OUT_0 Request a reset event (0 => forcesreset) 1 CHKSTOPOUT_0 Request that node 0 enter checkstop state (0 =>request checkstop) 2 CHKSTOPOUT_1 Request that node 1 enter checkstopstate (0 => request checkstop) 3 CHKSTOPOUT_2 Request that node 2 entercheckstop state (0 => request checkstop) 4 CHKSTOPOUT_3 Request thatnode 3 enter checkstop state (0 => request checkstop) 5 CHKSTOPOUT_8240Request that the host controller enter checkstop state (0 => requestcheckstop) 6 Software definable 0 Software definable 0 7 Softwaredefinable 1 Software definable 1

A single write of any value will strobe the watchdog. Upon events suchas power-up, the watchdogs are initialized to a fault state. Once avalid strobe is issued, the watchdog executes and, if all elements areproperly operating, writes a no-fault state to the HA register 212. Thisoccurs within the initial two-second period after board level reset. Ifa processor node fails to service the watchdog within the valid timeframe, the watchdog records a fault state. A watchdog of a compute node220 in fault triggers an interrupt to the host controller 203. If afault is within the host controller 203, then the watchdog triggers areset to the board. The watchdog then remains in a latched failed stateuntil a CPU reset occurs followed by a valid service sequence.

Each processor node ASIC 234 accesses a DIAG3 signal that is wired to anHA register, and is used to strobe the compute element's hardwarewatchdog monitor. A DIAG2 signal is wired to the host processor'sembedded programmable interrupt controller (EPIC) and is used by acompute element to generate a general purpose interrupt to the hostcontroller 203.

A majority voter (hereinafter “voter”) is a dual software sub-systemstate machine that identifies faults within each of the processors(e.g., the host controller 230 and each compute node 220 a–220 d) andalso of the processor board 118 itself. The local voter can resetindividual processors (e.g., a compute node 220) by asserting aCHECKSTOP_IN to that processor. The board level voter can force a resetof the board by asserting a master reset, wherein all processors arereset. Both voters follow a rule set that the output will follow themajority of non-checkstopped processors. If there are more processors ina fault condition than a non-fault condition, the voter will force aboard reset. Of course, other embodiments may use other rules, or canuse a single sub-system to accomplish the same purpose.

A majority voter is illustrated in FIG. 4. Board level resets areinitiated from a variety of sources. One such source is a voltagesupervisor (e.g., the power status/control device 240) which cangenerate a 200 ms reset if the voltage (e.g., VCC) rises above apredetermined threshold, such as 4.38 volts (this is also used in theillustrated embodiment in a pushbutton reset switch 406, however, thepush button can also be a separate signal). The board level voter willcontinue to drive a RESET_0 408 until both the voltage supervisor 404and the PCI_RESET_0 410 are dc-asserted. Either reset will generate thesignal RESET_0 412 which resets the card into a power-on state. RESET_0412 also generates HRESET_0 414 and TRST 416 signals to each processor.Further, a HRESET_0 and TRST can be generated by the JTAG ports using aJTAG_HRESET_0 418 and JTAG_TRST 420 respectively. The host controller203 can generate a reset request, a soft reset (C_SRESET_0 422) to eachprocessor, a cheek-stop request, and an ASIC reset (CE_RESET_0 424) toeach of the four compute element's ASIC. A discrete word from the 5v-powered reset PLD will generate the signal NPORESET_1 (not a power onreset). This signal is fed into the host processor discrete input word.The host processor will read this signal as logic low only if it iscoming out of reset due to either a power condition or an external resetfrom off board. Each compute element, as well as the host processor canrequest a board level reset. These requests are majority voted, and theresult RESET-VOTE_0 will generate a board level reset.

Each compute node processor 228 has a hard reset signal driven by threesources gated together: a HRESET_0 pin 426 on each ASIC, a HRESET_0 418from the JTAG connector 232, and a HRESET_0 412 from the majority voter.The HRESET_0 pin 426 from the ASIC is set by the “node run” bit field(bit 0) of the ASIC Miscon_A register. Setting HRESET_0 426 low causesthe node processor to be held in reset. HRESET_0 426 is low immediatelyafter system reset or power-up, the node processor is held in resetuntil the HRESET_0 line is pulled high by setting the node run bit to 1.The JTAG HRESET 0 418 is controlled by software when a JTAG debuggermodule is connected to the card. The HRESET_0 412 from the majorityvoter is generated by a majority vote from all healthy nodes to reset.

When a processor reset is asserted, the compute processor 228 is putinto reset state. The compute processor 228 remains in a reset stateuntil the RUN bit 0 of the Miscon_A register is set to 1 and the hostprocessor has released the reset signals in the discrete output word.The RUN bit is set to 1 after the boot code has been loaded into theSDRAM starting at location 0x0000_(—)0100. The ASIC maps the resetvector 0xFFF0_(—)0100 generated by the MPC7400 to address0x0000_(—)0100.

Turning now to discuss memory devices 205 coupled with the hostcontroller 203, the memory devices are addressable by the hostcontroller 203 as follows. The host controller 203 addresses the memorydevices (e.g., the HA registers 212, SDRAM 214, Flash 216 and NVRAM 218)using two address mapping configurations designated as address map A andaddress map B, although other configurations are possible. Address map Aconforms to the PowerPC reference platform (PrcP) specification(however, if other host controllers are used, map A conforms with anative reference platform to that host controller). Address map Bconforms to the host controller 203 common hardware reference platform(CHRP).

Support of map A is provided for backward compatibility, and furthersupports any retrofitting of existing base station configurations. Theaddress space of map B is divided into four areas: system memory, PCImemory, PCI Input/Output (I/O), and system ROM space. When configuredfor map B, the host controller translates addresses across the internalperipheral logic bus and the external PCI bus as follows:

Processor Core Address Range Hex Decimal PCI Address Range Definition0000_0000 0009_FFFF 0 640K - 1 NO PCI CYCLE System memory 000A_0000000F_FFFF 640K 1M-1 000A_0000–000F_FFFF Compatibility hole 0010_00003FFF_FFFF 1M 1G-1 NO PCI CYCLE System memory 4000_0000 7FFF_FFFF 1G 2G-1NO PCI CYCLE Reserved 8000_0000 FCFF_FFFF 2G 4G-48M-18000_0000–FCFF_FFFF PCI memory FD00_0000 FDFF_FFFF 4G-48M 4G-32M-10000_0000–00FF_FFFF PCI/ISA memory FE00_0000 FE7F_FFFF 4G-32M 4G-24M-10000_0000–007F_FFFF PCI/ISA I/O FE80_0000 FEBF_FFFF 4G-24M 4G-20M-10080_0000–00BF_FFFF PCI I/O FEC0_0000 FEDF_FFFF 4G-20M 4G-18M-1CONFIG_ADDR PCI configuration address FEE0_0000 FEEF_FFFF 4G-18M4G-17M-1 CONFIG_DATA PCI configuration data FEF0_0000 FEFF_FFFF 4G-17M4G-16M-1 FEF0_0000–FEFF_FFFF PCI interrupt acknowledge FF00_0000FF7F_FFFF 4G-16M 4G-8M-1 FF00_0000–FF7F_FFFF 32/64-bit Flash/ROMFF80_0000 FFFF_FFFF 4G-8M 4G-1 FF80_0000–FFFF_FFFF 8/32/64-bit Flash/ROM

In the illustrated embodiment, hex address FF00_(—)0000 throughFF7F_FFFF is not used, and hence, that bank of Flash ROM is not used.The address of FF80_(—)0000 through FFFF_FFFF is used, as the Flash ROMis configured in 8-bit mode and is addressed as follows:

Processor Core Bank Select Address Range Definition 11111 11110-FFE0_0000 FFEF_FFFF Accesses Bank 0 00001 FFE0_0000 FFEF_FFFFApplication code (30 pages) 00000 FFE0_0000 FFEF_FFFF Application/bootcode XXXX FFF0_0000 FFFF_CFFF Application/boot code FFFF_D000 FFFF_D000Discrete input word 0 FFFF_D001 FFFF_D001 Discrete input word 1FFFF_D002 FFFF_D002 Discrete output word 0 FFFF_D003 FFFF_D003 Discreteoutput word 1 FFFF_D004 FFFF_D004 Discrete output word 2 FFFF_D010FFFF_D010 IC (Pending interrupt) FFFF_D011 FFFF_D011 IC (Interrupt masklow) FFFF_D012 FFFF_D012 IC (Interrupt clear low) FFFF_D013 FFFF_D013 IC(Unmasked, pending low) FFFF_D014 FFFF_D014 IC (Interrupt input low)FFFF_D015 FFFF_D015 Unused (read FF) FFFF_D016 FFFF_D016 Unused (readFF) FFFF_D017 FFFF_D017 Unused (read FF) FFFF_D018 FFFF_D018 Unused(read FF) FFFF_D019 FFFF_D019 Unused (read FF) FFFF_D020 FFFF_D020 HA(Local HA register) FFFF_D021 FFFF_D021 HA (Node 0 HA register)FFFF_D022 FFFF_D022 HA (Node 1 HA register) FFFF_D023 FFFF_D023 HA (Node2 HA register) FFFF_D024 FFFF_D024 HA (Node 3 HA register) FFFF_D025FFFF_D025 HA (8240 HA register) FFFF_D026 FFFF_D026 HA (Software Fail)FFFF_D027 FFFF_D027 HA (Watchdog Strobe) FFFF_D028 FFFF_DFFF 4068 BytesFlash FFFF_E000 FFFF_FFFF 8K NVRAM

Address FFEF_(—)0000 through FFEF_FFFF contains 30 pages, and is usedfor application and boot code, as selected by the Flash bank bits.Further, there a 2 Mbyte block available after reset. Data movementoccurs on the PCI 211 a and/or a memory bus.

DMA Engine Supported by Host Controller and FPGA

Direct memory access (DMA) is performed by the host controller 203, andoperates independently from the host processor 203 core, as illustratedin FIG. 5. The host controller 203 has an integrated DMA engineincluding a DMA command stack 502, a DMA state engine 504, an addressdecode block 506, and three FIFO interfaces 508, 510, 512. The DMAengine receives and sends information via the PXB 208 coupled with thecrossbar 206.

The command stack 502 and state machine 504 processes DMA requests andtransfers. The stack 502 and state machine 504 can initiate both cyclestealing and burst mode, along with host controller interrupts. Theaddress decode 506 sets the bus address, and triggers transmissions ofthe data.

The host controller 203 has two DMA I/O interfaces, each with a 64-bytequeue to facilitate the gathering and sending of data. Both the localprocessor and PCI masters can initiate a DMA transfer. The DMAcontroller supports memory transfers between PCI to memory, betweenlocal and PCI memory, and between local memory devices. Further, thehost controller 203 can transfer in either block mode or scatter modewithin discontinuous memory. A receiving channel 510 buffers data thatis to be received by the memory. A transmit channel 512 buffers datathat is sent from memory. Of course, the buffers can also send/receiveinformation from other devices, e.g., the compute nodes 220, or otherdevices capable of DMA transfers.

The host controller 203 contains an embedded programmable interruptcontroller (EPIC) device. The interrupt controller implements thenecessary functions to provide a flexible and general-purpose interruptcontroller. Further, the interrupt controller can pool interruptsgenerated from the several external components (e.g., the computeelements), and deliver them to the processor core in a prioritizedmanner. In the illustrated embodiment, an OpenPIC architecture is used,although it can be appreciated by one skilled in the art that other suchmethods and techniques can be used. Here, the host controller 203supports up to five external interrupts, four internal logic-driveninterrupts, and four timers with interrupts.

Data transfers can also take effect via the FPGA program interface 508.This interface can program and/or accept data from various FPGAs, e.g.,the compute note ASIC 234, crossbar 242, and other devices. Datatransfers within the compute node processor 228 to its ASIC 234 andRACEway™ bus 246 are addressed as follows:

From Address To Address Function 0x0000 0000 0x0FFF FFFF Local SDRAM 256Mb 0x1000 0000 0x1FFF FFFF crossbar 256 Mb map window 1 0x2000 00000x2FFF FFFF crossbar 256 MB map window 2 0x3000 0000 0x3FFF FFFFcrossbar 256 MB map window 3 0x4000 0000 0x4FFF FFFF crossbar 256 MB mapwindow 4 0x5000 0000 0x5FFF FFFF crossbar 256 MB map window 5 0x60000000 0x6FFF FFFF crossbar 256 MB map window 6 0x7000 0000 0x7FFF FFFFcrossbar 256 MB map window 7 0x8000 0000 0x8FFF FFFF crossbar 256 MB mapwindow 8 0x9000 0000 0x9FFF FFFF crossbar 256 MB map window 9 0xA0000000 0xAFFF FFFF crossbar 256 MB map window A 0xB000 0000 0xBFFF FFFFcrossbar 256 MB map window B 0xC000 0000 0xCFFF FFFF crossbar 256 MB mapwindow C 0xD000 0000 0xDFFF FFFF crossbar 256 MB map window D 0xE0000000 0xEFFF FFFF crossbar 256 MB map window E 0xF000 0000 0xFBFF FBFFNot used (CE reg replicated mapping) 0xFBFF FC00 0xFBFF FDFF Internal CNASIC registers 0xFBFF FE00 0xFEFF FFFF Pre-fetch control 0xFF00 00000xFFFF FFFF 16 MB boot FLASH memory area

The SDRAM 236 can be addressable in 8, 16, 32 or 64 bit addresses. TheRACEway™ bus 246 supports locked read/write and locked read transactionsfor all data sizes. A 16 Mbyte boot flash area is further divided asfollows:

From Address To Address Function 0xFF00 2006 0xFF00 2006 Software FailRegister 0xFF00 2005 0xFF00 2005 MPC8240 HA Register 0xFF00 2004 0xFF002004 Node 3 HA Register 0xFF00 2003 0xFF00 2003 Node 2 HA Register0xFF00 2002 0xFF00 2002 Node 1 HA Register 0xFF00 2001 0xFF00 2001 Node0 HA Register 0xFF00 2000 0xFF00 2000 Local HA Register (status/control)0xFF00 0000 0xFF00 1FFF NVRAM

Slave accesses are accesses initiated by an external RACEway™ devicedirected toward the compute element processor 238. The ASIC 234 supportsa 256 Mbyte address space which can be partitioned as follows:

From Address To Address Function 0x0000 0000 0x0FFF FBFF 256 MB less 1Kb hole SDRAM 0Xfff_FC00 0xFFF_FFFF PCE133 internal registers

There are 16 discrete output signals directly controllable and readableby the host controller 203. The 16 discrete output signals are dividedinto two addressable 8-bit words. Writing to a discrete output registerwill cause the upper 8-bits of the data bus to be written to thediscrete output latch. Reading a discrete output register will drive the8-bit discrete output onto the tipper 8-bits of the host processor databus. The bits in the discrete output word are defined as follows:

There are 16 discrete input signals accessible by the host controller203. Reads from the discrete input address space will latch the state ofthe signals, and return the latched state of the discrete input signalsto the host processor. The bits in the discrete input word are asfollows:

Output Word 2 DH(0:7) Signal Description 0 ND0_FLASH_EN_1 Enable the CEASIC's FLASH port when 1 1 ND1_FLASH_EN_1 Enable the CE ASIC's FLASHport when 1 2 ND2_FLASH_EN_1 Enable the CE ASIC's FLASH port when 1 3ND3_FLASH_EN_1 Enable the CE ASIC's FLASH port when 1 4 Wrap 1 Wrap todiscrete input 5 6 7 Output Word 1 DH(0:7) Signal Description 0 WRAP0Wrap to Discrete Input 1 12C_RESET_0 Reset the 12C serial bus when 0 2SWLED Software controlled LED 3 FLASHSEL4 Flash bank select address bit4 4 FLASHSEL3 Flash bank select address bit 3 5 FLASHSEL2 Flash bankselect address bit 2 6 FLASHSEL1 Flash bank select address bit 1 7FLASHSEL0 Flash bank select address bit 0 Output Word 0 DH(0:7) SignalDescription 0 C_SRESET3_0 Issue a Soft Reset to CPU on Node 3 when 0 1C_PRESET3_0 Reset PCE133 ASIC Node 3 when 0 2 C_SRESET2_0 Issue a SoftReset to cpu on Node 2 when 0 3 C_PRESET2_0 Reset PCE133 ASIC Node 2when 0 4 C_SRESET1_0 Issue a Soft Reset to cpu on Node 1 when 0 5C_PRESET1_0 Reset PCE133 ASIC Node 1 when 0 6 C_SRESET0_0 Issue a SoftReset to cpu on Node 0 when 0 7 C_PRESET0_0 Reset PCE133 ASIC Node 0when 0 Output Word 1 DH(0:7) Signal Description 0 WRAP1 Wrap fromdiscrete output word 1 2 V3.3_FAIL_0 Latched status of power supplysince last reset 3 V2.5_FAIL_0 Latched status of power supply since lastreset 4 VCORE1_FAIL_0 Latched status of power supply since last reset 5VCORE0_FAIL_0 Latched status of power supply since last reset 6RIOR_CNF_DONE_1 RIO/RACE++ FPGA configuration complete 7 PXB0_CNF_DONE_1PXB++ FPGA configuration complete Input Word 0 DH(0:7) SignalDescription 0 WRAP0 Wrap from discrete output word 1 WDMSTATUS MPC8240'swatchdog monitor status (0 = failed) 2 NPORESET_1 Not a power on resetwhen high 3 4 5 6 7

The host controller 203 interfaces with an 8-input interrupt controllerexternal from processor itself (although in other embodiments it can becontained within the processor). The interrupt inputs are wired, throughthe controller to interrupt zero of the host processor externalinterrupt inputs. The remaining four host processor interrupt inputs areunused.

The Interrupt Controller comprises the following five 8-bit registers:

Resister Description Pending Register A low bit indicates a falling edgewas detected on that interrupt (read only); Clear Register Setting a bitlow will clear the corresponding latched interrupt (write only); MaskRegister Setting a bit low will mask the pending interrupt fromgenerating a processor interrupt; Unmasked Pending A low bit indicates apending interrupt Register that is not masked out Interrupt Stateindicates the actual logic level of each Register interrupt input pin.

The interrupt input sources and their bit positions within each of thesix registers are as follows:

Bit Signal Description 0 SWFAIL_0 8240 Software Controlled Fail Discrete1 RTC_INT_0 Real time clock event 2 NODE0_FAIL_0 WDFAIL_0 or IWDFAIL_0or SWFAIL_0 active 3 NODE1_FAIL_0 WDFAIL_0 or IWDFAIL_0 or SWFAIL_0active 4 NODE2_FAIL_0 WDFAIL_0 or IWDFAIL_0 or SWFAIL_0 active 5NODE3_FAIL_0 WDFAIL_0 or IWDFAIL_0 or SWFAIL_0 active 6 PCI_INT_0 PCIinterrupt 7 XB_SYS_ERR_0 crossbar internal error

A falling edge on an interrupt input will set the appropriate bit in thepending register low. The pending register is gated with the maskregister and any unmasked pending interrupts will activate the interruptoutput signal to the host processor external interrupt input pin.Software will then read the unmasked pending register to determine whichinterrupt(s) caused the exception. Software can then clear theinterrupt(s) by writing a zero to the corresponding bit in the clearregister. If multiple interrupts are pending, the software has theoption of either servicing all pending interrupts at once and thenclearing the pending register or servicing the highest priorityinterrupt (software priority scheme) and the clearing that singleinterrupt. If more interrupts are still latched, the interruptcontroller will generate a second interrupt to the host processor forsoftware to service. This will continue until all interrupts have beenserviced.

An interrupt that is masked will show up in the pending register but notin the unmasked pending register and will not generate a processorinterrupt. If the mask is then cleared, that pending interrupt will flowthrough the unmasked pending register and generate a processorinterrupt.

The multiple components within the processor board 118 dictate variouspower requirements. The processor board 118 requires 3.3V, 2.5V, and1.8V. In the illustrated embodiment, there are two processor corevoltage supplies 302, 304 each driving two 1.8V cores for two processors(e.g., 228). There is also a 3.3V supply 306 and a 2.5V supply 308 whichsupply voltage to the remaining components (e.g., crossbar 206,interface block 205 and so on). To provide power to the board, the threevoltages (e.g., the 1.8V, 3.3V and 2.5V) have separate switchingsupplies, and proper power sequencing. All three voltages are convertedfrom 5.0V. The power to the processor card 118 is provided directly fromthe modem board 112 within the base station, however, in otherembodiments there is a separate or otherwise integrated power supply.The power supply a preferred embodiment is rated as 12 A, however, inother embodiments the rating varies according to the specific componentrequirements.

In the illustrated embodiment, for instance, the 3.3V power supply 306is used to provide power to the NVRAM 218 core, SDRAM 214, PXB 208, andcrossbar ASIC 206 (or FPGA is present). This power supply is rated as afunction of the devices chosen for these functions.

A 2.5V power supply 308 is used to provide power to the compute nodeASIC 234 and can also power the PXB 208 FPGA core. The host processorbus can run at 2.5V signaling. The host bus can operate at 2.5Vsignaling.

The power-on sequencing is necessary in multi-voltage digital boards.One skilled in the art can appreciate that power sequencing is necessaryfor long-term reliability. The right power supply sequencing can beaccomplished by using inhibit signals. To provide fail-safe operation ofthe device, power should be supplied so that if the core supply failsduring operation, the I/O supply is shut down as well.

Although in theory, the general rule is to ramp all power supplies upand down at the same time as illustrated in FIG. 6. The ramp up 602 andramp down 604 show agreement with the power supplies 302, 304, 306, 308over time. One skilled in the art realizes that in reality, voltageincreases and decreases do not occur among multiple power supplies insuch a simultaneous fashion.

FIG. 7 shown the actual voltage characteristics for the illustratedembodiment. As 40 can be seen, ramp up 702 a–702 c and ramp down 704a–704 c sequences depend on multiple factors, e.g., power supply, totalboard capacities that need to be charged, power supply load, and so on.For example, the ramp up for the 3.3V supply 702 a occurs before theramp up for the 2.5V supply 702 c, which occurs before the ramp up ofthe 1.8V supplies 702 b. Further, the ramp down for the 3.3V supply 704a occurs before the ramp down for the 2.5V supply 704 c, which occursbefore the ramp down for the 1.8V supplies 704 c.

Also, The host processor requires the core supply to not exceed the I/Osupply by more than 0.4 volts at all times. Also, the I/O supply mustnot exceed the core supply by more than 2 volts. Therefore, to achievean acceptable power-up and power-down sequencing, e.g., to avoid damageto the components, a circuit containing diodes is used in conjunctionwith the power supplied within the base station.

The power status/control device 240 is designed from a programmablelogic device (PLD). The PLD is used to monitor the voltage statussignals from the on board supplies. It is powered up from +5V andmonitors +3.3V, +2.5V, 1.8V_(—)1 and +1.8V_(—)2. This device monitorsthe power_good signals from each supply. In the case of a power failurein one or more supplies, the PLD will issue a restart to all suppliesand a board level reset to the processor board. A latched power statussignal will be available from each supply as part of the discrete inputword. The latched discrete can indicate any power fault condition sincethe last off-board reset condition.

In operation, the processor board inputs raw antenna data from the basestation modem card 112 (or other available location of that data),detects sources of interference within that data, and produces a newstream of data which has reduced interference subsequently transmittingthat refined data back to the modem card (or other location) for furtherprocessing within the base station.

As can be appreciated by one skilled in the art, such interferencereduction is computationally complex; hence, the hardware must supportthroughputs sufficient for multiple user processing. In a preferredembodiment, characteristics of processing are a latency of less than 300microseconds handing data in the 110 Mbytes/Sec range, however, in otherembodiments the latency and data load can vary.

In the illustrated embodiment, data from the modem board is supplied viathe PCI bus 211 b through the PCI bridge 222. From there, the datatraverses the crossbar 206 and is loaded into the host controller memory205. Output data flows in the opposite direction. Additionally, certaindata flows between the host controller 203 and the compute elements 220.

Hybrid Operating System

The compute elements 220 operate, in some embodiments, under the MC/OSoperating system available commercially from the assignee herein,although different configurations can run under different operatingsystems suited for such. Here, one aspect is to reduce the use ofnon-POSIX system calls which can increase portability of the multipleuser detection software among different hardware environments andoperating system environments. The host processor is operated by theVxWorks operating system, as is required by MC/OS and suitable for aMotorola 8240 PowerPC.

FIG. 8 shows a block diagram of various components within thehardware/software environment. An MC/OS subsystem 802 is used as anoperating system for the compute elements 220. Further, a MC/OS DX 804provides APIs acceptable overhead and latency access to the DMA engineswhich in turn provide suitable bandwidth transfers of data. DX 804 canbe used to move data between the compute elements 220 during parallelprocessing, and also to move data between the compute elements 220, thehost controller 203, and the modem card 112. As described above, eachcompute element 220 continues an application 806, and a watchdog 808.Further, the HA registers provide the bootstrap 810 necessary forstart-up.

The host controller 203 runs under the VxWorks operating system 812. Thehost processor 202 contains a watchdog 814, application data 816, and abootstrap 818. Further, the host processor 202 can perform TCP/IP stackprocessing 820 for communication through the Ethernet interface 224.

Input/output between the processor card 118 and the modem card 112 takesplace by moving data between the Race++ Fabric and the PCI bus 211 b viathe PCI bridge 222. The application 806 will use DX to initialize thePXB++ bridge, and to cause input/output data to move as if it wereregular DX IPC traffic. For example, there are several components whichcan initiate data transfers and choose PCI addresses to be involved withthe transfers.

One approach to increasing available on the processor card 118 is tobalance host-processing time against application execution. For example,when the system comes up, the application determines which processingresources are available, and the application determines a load mappingon the available resources and record certain parameters in NVRAM.Although briefs interruptions in service can occur, the application doesnot need to know how to continue execution across faults. For instance,the application can make an assumption that the hardware configurationwill not change without the system first rebooting. If the applicationis in a state which needs to be preserved across reboots, theapplication checkpoints the data on a regular basis. The system softwareprovides an API to a portion of the NVRAM for this purpose

The host controller 203 is attached to an amount of linear flash memory216 as discussed above. This flash memory 216 serves several purposes.The first purpose the flash memory serves is as a source of instructionsto execute when the host controller comes out of reset. Linear flash canbe addressed much like normal RAM. Flash memories can be organized tolook like disk controllers; however in that configuration they generallyrequire a disk driver to provide access to the flash memory. Althoughsuch an organization has several benefits such as automatic reallocationof bad flash cells, and write wear leveling, it is not appropriate forinitial bootstrap. The flash memory 216 also serves as a file system forthe host and as a place to store permanent board information (e.g., suchas a serial number).

When the host controller 203 first comes out of reset, memory is notturned on. Since high-level languages such as C assume some memory ispresent (e.g., for a stack) the initial bootstrap code must be coded inassembler. This assembler bootstrap contains a few hundred lines ofcode, sufficient to configure the memory controller, initialize memory,and initialize the configuration of the host processor internalregisters.

After the assembler bootstrap has finished execution, control is passedto the processor HA code (which is also contained in boot flash memory).The purpose of the HA code is to attempt to configure the fabric, andload the compute element CPUs with HA code. Once this is complete, allthe processors participate in the HA algorithm. The output of thealgorithm is a configuration table which details which hardware isoperational and which hardware is not. This is an input to the nextstage of bootstrap, the multi-computer configuration.

MC/OS expects the host controller system to configure the multi-computer(e.g., compute elements 220). A configmc program reads a textualdescription of the computer system configuration, and produces a seriesof binary data structures that describe the system configuration. Thesedata structures are used in MC/OS to describe the routing andconfiguration of the multi-computer.

The processor board 118 will use almost exactly the same sequence toconfigure the multi-computer. The major difference is that MC/OS expectsconfigurations to be static, whereas the processor board configurationchanges dynamically as faulty hardware cause various resources to beunavailable for use.

One embodiment of the invention uses binary data structures produced byconfigmc to modify flags that indicate whether a piece of hardware isusable. A modification to MC/OS prevents it from using hardware markedas broken. Another embodiment utilizes the output of the HA algorithm toproduce a new configuration file input to configmc, the configmcexecution is repeated with the new file, and MC/OS is configured andloaded with no knowledge of the broken hardware whatsoever. Thisembodiment can calculate an optimal routing table in the face of failedhardware, increasing the performance of the remaining operationalcomponents.

After the host controller has configured the compute elements 220, therunme program loads the functional compute elements with a copy ofMC/OS. Because access to the processor board 118 from a TCP/IP networkis required, the host computer system acts as a connection to the TCP/IPnetwork. The VxWorks operating system contains a fully functional TCP/IPstack. When compute elements access network resources, the host computeracts as proxy, exchanging information with the compute element utilizingDX transfers, and then making the appropriate TCP/IP calls on behalf ofthe compute element.

The host controller 203 needs a file system to store configurationfiles, executable programs, and MC/OS images. For this purpose, flashmemory is utilized. Rather than have a separate flash memory from thehost controller boot flash, the same flash is utilized for bothbootstrap purposes and for holding file system data. The flash filesystem provides DOS file system semantics as well as write wearleveling.

There are in particular, two portions of code which can be remotelyupdated; the bootstrap code which is executed by the host controller 203when it comes out of reset, and the rest of the code which resides onthe flash file system as files.

When code is initially downloaded to the processor board 118, it iswritten as a group of files within a directory in the flash file system.A single top-level index tracks which directory tree is used for bootingthe system. This index continues to point at the existing directory treeuntil a download of new software is successfully completed. When adownload has been completed and verified, the top-level index is updatedto point to the new directory tree, the boot flash is rewritten, and thesystem can be rebooted.

Fault detection and reporting 820, 822 is performed by having each CPUin the system gather as much information about what it observed during afault, and then comparing the information in order to detect whichcomponents could be the common cause of the symptoms. In some cases, itmay take multiple faults before the algorithm can detect which componentis at fault.

Failures within the processor board 118 can be a single point failure.Specifically, everything on the board is a single point of failureexcept for the compute elements. This means that the only hard failuresthat can be configured out are failures in the compute elements 220.However, many failures are transient or soft, and these can be recoveredfrom with a reboot cycle.

In the case of hard failure of a compute element 220, the applicationexecutes with reduced demand for computing resources. For example, theapplication may work with a smaller number of interference sources, orperform interference cancellation iterations, but still within atolerance.

Failure of more than a single compute element will cause the board to beinoperative. Therefore, the application only needs to handle twoconfigurations: all compute elements functional and 1 compute elementunavailable. Note that the single crossbar means that there are noissues as to which processes need to go on which processors—thebandwidth and latencies for any node to any other node are identical onthe processor board, although other methods and techniques can be used.

DSP Connected to Processing Board

FIG. 9 shows an embodiment of the invention wherein a digital signalprocessor (DSP) 900 is connected with the processor board 118. Suchconfiguration enables a DSP to communicate via DMA with processor board.One skilled in the art can appreciate that DMA transfers can be fasterthan bus transfers, and hence, throughput can be increased. Shown, is aDSP processor, a buffer, a FPGA and a crossbar.

The DSP 900 generates a digital signal corresponding to an analog input,e.g., a rake receiver. The DSP 900 operates in real-time, hence, theoutput is clocked to perform transfers of the digital output. In theillustrated embodiment, the DSP can be a Texas Instruments modelTMS320C67XX series, however, other DSP processors are commerciallyavailable which can satisfy the methods and systems herein.

A buffer 902 is coupled with the DSP 900, and receives and send data ina First-In First-Out (e.g., queue) fashion, also referred to as a FIFObuffer. The buffer 902, in some embodiments, can be dual-ported RAM ofsufficient size to capture data transfers. One skilled in the art canappreciate, however, that a protocol can be utilized to transfer thedata where the buffer or dual-ported RAM is smaller that the datatransfer size.

A FPGA 904 is coupled with both the buffer 902 and an crossbar 906(which can be the same crossbar coupled with the compute elements 220and host controller 203). The FPGA 904 moves data from the buffer 902 tothe crossbar 906, which subsequently communicates the data to furtherdevices, e.g., a RACEway™ or the host controller 203 or compute elements220. The FPGA 904 also perform data transfers directly from the DSP 900to the crossbar 906. This method is utilized in some embodiments wheredata transfer sizes can be accommodated without buffering, for instance,although either the buffer or direct transfers can be used.

The DSP 900 contains at least one external memory interface (EMIF) 908device, which is connected to the buffer 902 or dual-ported RAM.RACEway™ transfers actually access the RAM, and then additionalprocessing takes place within the DSP to move the data to the correctlocation in SDRAM within the DSP. In embodiments where the RAM issmaller that the data transfer size, then there is a massaging protocolbetween two endpoint DSPs exchanging messages, since the message will befragmented to be contained within the buffer or RAM.

As more RACEway™ endpoints are added (for instance, to increase speed orthrough-put), the size of the dual-port RAM can be increased to a sizeof 2*F*N*P buffers of size F, where F is the fragment size, N is thenumber of RACEway™ endpoints in communication with the DSP, and P is thenumber of parallel transfers which can be active on an endpoint. Theconstant 2 represents double buffering so one buffer can be transferredto the RACEway™ simultaneously with a buffer being transferred to theDSP. One skilled in the art can appreciate that the constant can be fourtimes rather than two times to emulate a full-duplex connection. With a4 mode system, this could be, for example, 4*8K*4*4 or 512 Kbytes, plusa overhead factor for configuration and data tracking.

The FPGA 904 can program the DMA controller 910 within the DSP 900 tomove data between the buffer 902 and the DSP/SDRAM 912 directly from aDSP host port 914. The host port 914 is a peripheral like the EMIF 908,but can master transfers into the DSP data-paths, e.g., it can read andwrite any location within the DSP. Hence, the host port 914 can accessthe DMA controller, 910 and can be used to initiate transfers via theDMA engine. One skilled in the art can appreciate that using thisarchitecture, RACEway™ transfers can be initiated without thecooperation of the DSP, the thus, the DSP is free to continue processingwhile transfers take place and further, there is no need for protocolmessaging within the buffer.

The FPGA 904 can also perform fragmentation of data. In embodimentswhere the buffer device is a dual-port RAM, the FPGA 904 an program theDMA controller within the DSP to move fragments into or out-of the DSP.This method can be used to match throughput of the external transferbus, e.g., the RACEway™.

An example of the methods and systems described for a DSP, is asfollows. In an embodiment where the RACEway™ reads date out of the DSPmemory 912, this example assumes that another DSP is reading the SDRAMof the local DSP. The FPGA 904 detects a RACEway™ data packet arriving,and decodes the packet to determine that is contains instructions for adata-read at, for example, memory location 0x10000. The FPGA 904 writesover the host port interface 914 to program the DMA controller 910 totransfer data starting at memory location 0x10000, which refers to alocation in the primary EMIF 908 corresponding to a location in theSDRAM 912, and to move that data to a location in the secondary EMIF(e.g., the buffer device) 902. As data arrives in the buffer 902, theFPGA 904 reads the data out of the buffer, and moves it onto theRACEway™ bus. When a predetermined block of data is moved, the DMAcontroller 910 finishes the transfer, and the FPGA 904 finishes movingthe data from the buffer 902 to the RACEway™.

Another example assumes that another DSP is requesting a writeinstruction to the local DSP. Here, the FPGA 904 detects a data packetarriving, and determines that is it a write to location 0x20000, forinstance. The FPGA 904 fills some amount of the buffer 902 with the datafrom the RACEway™ bus, and then writes over the host port 914 interfaceto program the DMA controller 910. The DMA controller 910 then transfersdata from the buffer device 902 and writes that data to the primary EMIF908 at address 0x20000. At the conclusion of the transfer, an interruptcan be sent to the DSP 900 to indicate that a data packet has arrived,or a polling of a location in the SDRAM 912 can accomplish the samerequirement.

These two examples are non-limiting example, and other embodiments canutilize different methods and devices for the transfer of data betweendevices. For example, if the DSP 900 utilizes RapidIO interfaces, thebuffer 902 and FPGA 904 can be modified to accommodate this protocol.Also, the crossbar 906 illustrated may be in common with a separate busstructure, or be in common with the processor board 118 described above.Even further, in some embodiments, the FPGA 904 can be directly coupledwith the board processor, or be configured as a compute node 220.

Therefore, as can be understood by one skilled in the art, the methodsand systems herein are suited for multiple user detection within basestations, and can be used to accommodate both short-code and long-codereceivers.

Short-Code Processing

In one embodiment of the invention using short-code receivers, apossible mapping of matrices necessary for short-code mapping is nowdiscussed. In order to perform MUD at the symbol rate, the correlationbetween the user channel-corrupted signature waveform must becalculated. These correlations are stored as elements in matrices, herereferred to as R-matrices. Because the channel is continually changing,the correlations need be updated in realtime.

The implementation of MUD at the symbol rate can be divided into twofunctions. The first function is the calculation of the R-matrixelements. The second function is interference cancellation, which relieson knowledge of the R-matrix elements. The calculation of these elementsand the computational complexity are described in the following section.Computational complexity is expressed in Giga-Operations Per Second(GOPS). The subsequent section describes the MUD IC function. The methodof interference cancellation employed is Multistage Decision Feedback IC(MDFIC).

The R-matrix calculations can be divided into three separatecalculations, each with an associated time constant for real-timeoperation, as follows:

$\begin{matrix}{{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\;{e\left\lbrack {a_{l\; q}^{*}{a_{k\; q} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{\sum\limits_{p}{g\left\lbrack {{\left( {n - p} \right)N_{c}} + {m^{\prime}T} +} \right.}}}} \right.}}}}} \\{{\left. {\tau_{l\; q} - \tau_{l\; q^{\prime}}} \right\rbrack}{{c_{k}\lbrack p\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}} \\{= {{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\;{e\left\lbrack {a_{l\; q}^{*}{a_{k\; q} \cdot {c_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack}}} \right\rbrack}}}}}} \\{{C_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{p}{{g\left\lbrack {{\left( {n - p} \right)N_{c}} + {m^{\prime}T} + \tau_{l\; q} - \tau_{l\; q^{\prime}}} \right\rbrack}{{c_{k}\lbrack p\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}}}} \\{= {~~}{\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{p}{g\left\lbrack {{m\; N_{c}} + {m^{\prime}T} +} \right.}}}}} \\{{\left. {\tau_{l\; q} - \tau_{l\; q^{\prime}}} \right\rbrack}{\sum\limits_{n}{{c_{k}\left\lbrack {n - m} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{p}{{g\left\lbrack {{m\; N_{c}} + {m^{\prime}T} + \tau_{l\; q} - \tau_{l\; q^{\prime}}} \right\rbrack}{\Gamma_{l\; k}\lbrack m\rbrack}}}}}} \\{{\Gamma_{l\; k}\lbrack m\rbrack} = {\sum\limits_{n}{{c_{k}\left\lbrack {n - m} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}\end{matrix}$

Where the hats are omitted otherwise indicating parameter estimates.Hence we must calculate the R-matrices, which depend on the C-matrices,which in turn, depend on the Γ-matrix. The Γ-matrix has the slowest timeconstant. This matrix represents the user code correlations for allvalues of offset m. For a case of 100 voice users the total memoryrequirement is 21 MBytes based on two bytes (real and imaginary parts)per element. This matrix is updated only when new codes (e.g., newusers) are added to the system. Hence this is essentially a staticmatrix. The computational requirements are negligible.

The most efficient method of calculation depends on the non-zero lengthof the codes. For high data-rate users the non-zero length of the codesis only 4-chips long. For these codes, a direct convolution is the mostefficient method to calculation the elements. For low data-rate users itis more efficient to calculation the elements using the FFT to performthe convolutions in the frequency domain. Further, as can be appreciatedby one skilled in the art, cache memory can be used where the matrix issomewhat static compared with the update of other matrices.

The C-matrix is calculated from the Γ-matrix. These elements must becalculated whenever a user's delay lag changes. For now, assume that onaverage each multi-path component changes every 400 ms. The length ofthe g[ ] function is 48 samples. Since we are over sampling by 4, thereare 12 multiply-accumulations (real x complex) to be performed perelement, or 48 operations per element. When there are 100 low-rate userson the system (i.e., 200 virtual users) and a single multi path lag (of4) changes for one user a total of (1.5)(2)KvLNv elements must becalculated. The factor of 1.5 comes from the 3 C-matrices (m′=−1, 0, 1),reduced by a factor of 2 due to a conjugate symmetry condition. Thefactor of 2 results because both rows and columns must be updated. Thefactor Nv is the number of virtual users per physical user, which forthe lowest rate users is Nv=2. In total then this amounts to 230,400operations per multi-path component per physical user. Assuming 100physical users with 4 multi-path components per user, each changing onceper 400 ms gives 230 MOPS.

The R-matrices are calculated from the C-matrices. From the equationabove the R-matrix elements are

${r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {{\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\;{e\left\lbrack {a_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot {c_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack}}} \right\rbrack}}}} = {R\;{e\left\lbrack {a_{l}^{H} \cdot {C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k}} \right\rbrack}}}$

where a_(k) are L×l vectors, and C_(lk)[m′] are L×L matrices. The rateat which these calculations must be performed depends on the velocity ofthe users. The selected update rate is 1.33 ms. If the update rate istoo slow such that the estimated R-matrix values deviate significantlyfrom the actual R-matrix values then there is a degradation in the MUDefficiency.

From the above equation the calculation of the R-matrix elements can becalculated in terms of an X-matrix which represents amplitude-amplitudemultiplies:

$\begin{matrix}{{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {{R\;{e\left\lbrack {t\;{r\left\lbrack {a_{l}^{H} \cdot {C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k}} \right\rbrack}} \right\rbrack}} = {R\;{e\left\lbrack {t\;{r\left\lbrack {{C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k} \cdot a_{l}^{H}} \right\rbrack}} \right\rbrack}}}} \\{= {R\;{e\left\lbrack {t\;{r\left\lbrack {{C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot X_{l\; k}} \right\rbrack}} \right\rbrack}}} \\{= {{t\;{r\left\lbrack {{C_{l\; k}^{R}\left\lbrack m^{\prime} \right\rbrack} \cdot X_{l\; k}^{R}} \right\rbrack}} - {t\;{r\left\lbrack {C_{l\; k}^{l} \cdot X_{l\; k}^{l}} \right\rbrack}}}} \\{X_{l\; k} \equiv {a_{k} \cdot a_{l}^{H}} \equiv {X_{l\; k}^{R} + {j\; X_{l\; k}^{l}}}} \\{{C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \equiv {{C_{l\; k}^{R}\left\lbrack m^{\prime} \right\rbrack} + {j\;{C_{l\; k}^{l}\left\lbrack m^{\prime} \right\rbrack}}}}\end{matrix}\quad$

The X-matrix multiplies can be reused for all virtual users associatedwith a physical user and for all m′(i.e. m′=0, 1). Hence thesecalculations are negligible when amortized. The remaining calculationscan be expressed as a single real dot product of length 2L 2=32. Thecalculations are performed in 16-bit fixed-point math. The totaloperations is thus 1.5(4)(KvL)2 =3.84 Mops. The processing requirementis then 2.90 GOPS. The X-matrix multiplies when amortized amount to anadditional 0.7 GOPS. The total processing requirement is then 3.60 GOPS.

From the equation above the matched-filter outputs are given by:

${y_{l}\lbrack m\rbrack} = {{{r_{l\; l}\lbrack 0\rbrack}{b_{l}\lbrack m\rbrack}} + {\sum\limits_{k = 1}^{K_{y}}{{r_{l\; k}\left\lbrack {- 1} \right\rbrack}{b_{k}\left\lbrack {m + 1} \right\rbrack}}} + {\sum\limits_{k = 1}^{K_{y}}{\left\lbrack {{r_{l\; k}\lbrack 0\rbrack} - {{r_{l\; l}\lbrack 0\rbrack}\delta_{l\; k}}} \right\rbrack{b_{k}\lbrack m\rbrack}}} + {\sum\limits_{k = 1}^{K_{y}}{{r_{l\; k}\lbrack 1\rbrack}{b_{k}\left\lbrack {m - 1} \right\rbrack}}} + {\eta_{l}\lbrack m\rbrack}}$

The first term represents the signal of interest. All the remainingterms represent Multiple Access Interference (MAI) and noise. Themultiple-stage decision-feedback interference cancellation (MDFIC)algorithm iteratively solves for the symbol estimates using

${{\hat{b}}_{l}\lbrack m\rbrack} = {{sign}\left\{ {{y_{l}\lbrack m\rbrack} - {\sum\limits_{k = 1}^{K_{v}}{{r_{lk}\left\lbrack {- 1} \right\rbrack}{{\hat{b}}_{k}\left\lbrack {m + 1} \right\rbrack}}} - {\sum\limits_{k = 1}^{K_{v}}{\left\lbrack {{r_{lk}\lbrack 0\rbrack} - {{r_{ll}\lbrack 0\rbrack}\delta_{lk}}} \right\rbrack{{\hat{b}}_{k}\lbrack m\rbrack}}} - {\sum\limits_{k = 1}^{K_{v}}{{r_{lk}\lbrack 1\rbrack}{{\hat{b}}_{k}\left\lbrack {m - 1} \right\rbrack}}}} \right\}}$

with initial estimates given by hard decisions on the matched-filterdetection statistics, {circumflex over (b)}_(l)[m]=sign{y_(l)[m]}. TheMDFIC technique is closely related to the SIC and PIC technique. Noticethat new estimates are immediately introduced back into the interferencecancellation as they are calculated. Hence at any given cancellationstep the best available symbol estimates are used. This idea isanalogous to the Gauss-Siedel method for solving diagonally dominantlinear systems.

The above iteration is performed on a block of 20 symbols, for allusers. The 20-symbol block size represents two WCDMA time slots. TheR-matrices are assumed to be constant over this period. Performance isimproved under high input BER if the sign detector in is replaced by thehyperbolic tangent detector. This detector has a single slope parameterwhich is variable from iteration to iteration. Similarly, performance isimproved if only a fraction of the total estimated interference iscancelled (e.g., partial interference cancellation), owing to channeland symbol estimation errors.

Multiple Processors Generating Complementary R-Matrices

The three R-matrices (R[−1], R[0] and R[1]) are each Kv×Kv in size. Thetotal number of operation then is 6K_(v) ² per iteration. Thecomputational complexity of the multistage MDFIC algorithm depends onthe total number of virtual users, which depends on the mix of users atthe various spreading factors. For Kv=200 users (e.g. 100 low-rateusers) this amounts to 240,000 operations. In the current implementationtwo iterations are used, requiring a total of 480,000 operations. Forreal-time operation these operations must be performed in 1/15 ms. Thetotal processing requirement is then 7.2 GOPS. Computational complexityis markedly reduced if a threshold parameter is set such that IC isperformed only for values |y_(l)[m]| below the threshold. The idea isthat if |y_(l)[m]| is large there is little doubt as to the sign ofb_(l)[m], and IC need not be performed. The value of the thresholdparameter is variable from stage to stage.

Although three R matrices are output from the R matrix calculationfunction, only half of the elements are explicitly calculated. This isbecause of symmetry that exists between R matrices:R _(l,k) =ξR _(k,l)(−m)

Therefore, only two matrices need to be calculated. The first one is acombination of R(1) and R(−1). The second is the R(0) matrix. In thiscase, the essential R(0) matrix elements have a triangular structure tothem. The number of computations performed to generate the raw data forthe R(1)/R(−1) and R(0) matrices are combined and optimized as a singlenumber. This is due to the reuse of the X-matrix outer product valuesacross the two R-matrices. Since the bulk of the computations involvecombining the X-matrix and correlation values, they dominate theprocessor utilization. These computations are used as a cost metric indetermining the optimum loading of each processor.

Processor Loading Optimization

The optimization problem is formulated as an equal area problem, wherethe solution results in each partition area to be equal. Since the majordimensions of the R-matrices are in terms of the number of activevirtual users, the solution space for this problem is in terms of thenumber of virtual users per processor. By normalizing the solution spaceby the number of virtual users, the solution is applicable for anarbitrary number of virtual users.

FIG. 10 shows a model of the normalized optimization scenario. Thecomputations for the R(1)/R(−1) matrix are represented by the squareHJKM, while the computations for the R(0)matrix are represented by thetriangle ABC. From geometry, the area of a rectangle of length b andheight h is:A _(r) =bh

For a triangle with a base width b and height h, the area is calculatedby:

$A_{i} = {\frac{1}{2}{bh}}$

When combined with a common height a, the formula for the area becomes:

$\begin{matrix}{A_{i} = {A_{ri} + A_{ii}}} \\{= {{a_{i}a_{e}} + {\frac{1}{2}a_{i}^{2}}}}\end{matrix}$

The formula for A gives the area for the total region below thepartition line. For example, the formula for A2 gives the area withinthe rectangle HQRM plus the region within triangle AFG. For the costfunction, the difference in successive areas is used. That is:

$\begin{matrix}{B_{i} = {A_{i} - A_{i - 1}}} \\{= {{\frac{1}{2}a_{i}^{2}} + a_{i} - {\frac{1}{2}a_{i - 1}^{2}} - a_{i - 1}}}\end{matrix}$

For an optimum solution, the B must be equal for i=1,2, . . . , N, whereN is the number of processors performing the calculations. Because thetotal normalized load is equal to AN, the loading per processor load isequal to AN/N,

${B_{i} = {\frac{A_{N}}{N} = {\frac{A_{3}}{3} = \frac{3}{2N}}}},{{{for}\mspace{20mu} i} = 1},{2\mspace{14mu}\ldots}\mspace{11mu},{N.}$

By combining the two equations for B, the solution for a_(i) is found byfinding the roots of the equation:

${{\frac{1}{2}a_{i}^{2}} + a_{i} - {\frac{1}{2}a_{i - 1}^{2}} - a_{i - 1} - \frac{3}{2N}} = {0 < {{The}\mspace{14mu}{solution}\mspace{14mu}{for}\mspace{14mu} a\mspace{14mu}{is}\text{:}}}$${a_{i} = {{- 1} \pm \sqrt{1 + a_{{- 1}i}^{2} + {2a_{i - 1}} + \frac{3}{N}}}},{{{for}\mspace{14mu} i} - 1},2,\ldots\mspace{11mu},N$

Since the solution space must fall in the range [0,1], negative rootsare not valid solutions to the problem. On the surface, it appears thatthe a must be solved by first solving for case where =1. However, byexpanding the recursions of the a and using the fact that a0 equalszero, a solution that does not require previous a,=0,1, . . . ,n−1exists. The solution is:

$a_{i} = {{- 1} + \sqrt{1 + \frac{3i}{N}}}$

As shown in the following table, the normalized partition values fortwo, three, and four processors. To calculate the actual partitioningvalues, the number of active virtual users is multiplied by thecorresponding table entries. Since a fraction of a user cannot beallocated, a ceiling operation is performed that biases the number ofvirtual users per processor towards the processors whose loadingfunction is less sensitive to perturbations in the number of users.

Location Two Processors Three Processors Four Processors a₁${- 1} + {\sqrt{\frac{5}{2}}(0.5811)}$ ${- 1} + {\sqrt{2}(0.4142)}$${- 1} + {\sqrt{\frac{7}{4}}(0.3229)}$ a₂ — ${- 1} + {\sqrt{3}(0.7321)}$${- 1} + {\sqrt{\frac{5}{2}}(0.5811)}$ a₃ — —${- 1} + {\sqrt{\frac{13}{4}}(0.8028)}$

One skilled in the art can appreciate that the load balancing for theR-matrix results in a non-uniform partitioning of the rows of the finalmatrices over a number of processors. The partition sizes increase asthe partition starting user index increases. When the system is runningat full capacity (e.g., all co-processors are functional, and themaximum number of users is processed while still within the bounds ofreal-time operation), and a co-processor fails, the impact can besignificant.

This impact can be minimized by allocating the first user partition tothe disabled node. Also the values that would have been calculated bythat node are set to zero. This reduces the effects of the failed node.By changing which user data is set to zero (e.g., which users areassigned to the failed node) the overall errors due to the lack ofnon-zero output data for that node are averaged over all of the users,providing a “soft” degradation.

R, C Values Contiguous in MPIC Processor Memory

Further, via connection with the crossbar multi-port connector, themulti-processor elements calculating the R-matrix (which depends on theC-matrix, which in turn depends on the gamma-matrix) can place theresults in a processor element performing the MPIC functions. For oneoptimal solution, the values can be placed in contiguous locationsaccessable (or local with) the MPIC processor. This method allowsadjacent memory addresses for the R and C values, and increasesthroughput via simply incrementing memory pointers rather that using arandom access approach.

As discussed above, the values of the Γ-matrix elements which arenon-zero need to be determined for efficient storage of the Γ-matrix.For high data rate users, certain elements c_(l)[n] are zero, evenwithin the interval n=0:N−1, N=256. These zero values reduce theinterval over which Γ_(lk)[m] is non-zero. In order to determine theinterval for non-zero values consider the following relations:

${\Gamma_{lk}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N - 1}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}$

The index j_(l) for the lth virtual user is defined such that c_(l)[n]is non-zero only over the interval n=j_(l)N_(l): j_(l)N_(l)+N_(l)−1.Correspondingly, the vector c_(k)[n] is non-zero only over the intervaln=j_(k)N_(k): j_(k)N_(k)+N_(k)−1. Given these definitions, Γ_(lk)[m] canbe rewritten as

${\Gamma_{lk}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N_{l} - 1}{{c_{l}^{*}\left\lbrack {n + {j_{l}N_{l}}} \right\rbrack} \cdot {c_{k}\left\lbrack {n + {j_{l}N_{l}} - m} \right\rbrack}}}}$

The minimum value of m for which Γ_(lk)[m] is non-zero ism _(min2) =−j _(k) N _(k) +j _(l) N _(l) −N _(k)+1

and the maximum value of m for which Γ_(lk)[m] is non-zero ism _(max2) =N _(l)−1−j _(k) N _(k) +j _(l) N _(l)

The total number of non-zero elements is then

$\begin{matrix}{m_{total} \equiv {m_{\max\; 2} - m_{\min\; 2} + 1}} \\{= {N_{l} + N_{k} - 1}}\end{matrix}$

The table below provides a sample of the number of bytes per l,kvirtual-user pair based on 2 bytes per element—one byte for the realpart and one byte for the imaginary part. In other embodiments, thesevalues vary.

N_(k) = 256 128 64 32 16 8 4 N_(l) = 256 1022 766 638 574 542 526 518128 766 510 382 318 286 270 262  64 638 382 254 190 158 142 134  32 574318 190 126 94 78 70  16 542 286 158 94 62 46 38  8 526 270 142 78 46 3022  4 518 262 134 70 38 22 14

The memory requirements for storing the Γ-matrix for a given number ofusers at each spreading factor can be determined as described below. Forexample, for K_(q) virtual users at spreading factor N_(q)≡2^(8−q),q=0:6, where K_(q) is the qth element of the vector K (some elements ofK may be zero), the storage requirement can be computed as follows. Letthe table above be stored in matrix M with elements M_(qq). For example,M₀₀=1022, and M₀₁=766. The total memory required by the Γ matrix inbytes is then given by the following relation

$\begin{matrix}{\begin{matrix}{M_{bytes} = {\sum\limits_{q = 0}^{6}\left\{ {{\frac{K_{q}\left( {K_{q} + 1} \right)}{2}M_{qq}} + {\sum\limits_{q^{\prime} = \;{q + 1}}^{6}{K_{q}K_{q^{\prime}}M_{q\; q^{\prime}}}}} \right\}}} \\{= {\frac{1}{2}{\sum\limits_{q = 0}^{6}\left\{ {{K_{q}M_{q\; q}} + {\sum\limits_{q^{\prime} = \; 0}^{6}{K_{q}K_{q^{\prime}}M_{q\; q^{\prime}}}}} \right\}}}}\end{matrix}\quad} & (27)\end{matrix}$

Then, continuing the example, for 200 virtual users at spreading factorN₀=256, K_(q)=200δ_(q0), which in turn results inM_(bytes)=½K₀(K₀+1)M₀₀=100(201)(1022)=20.5 MB. For 10 384 Kbps users ,K_(q)=K₀δ_(q0)+K₆δ_(q6) with K₀=10 and K₆=640, which results in astorage requirement that is given by the following relations:M _(bytes)=½K₀(K ₀+1)M ₀₀ +K ₀ K ₆ M ₀₆+½K ₆(K ₆+1)M₆₆=5(11)(1022)+10(640)(518)+320(641)(14)=6.2 MB.

The Γ-matrix data can be addressed, stored, and accessed as describedbelow. In particular, for each pair (l,k), k>=l, there are 1 complexΓ_(lk)[m] values for each value of m, where in ranges from m_(min2) tom_(max2), and the total number of non-zero elements ism_(total)=m_(max2)−m_(min2)+l. Hence, for each pair (l,k), k>=l, thereexists 2m_(total) time-contiguous bytes.

In one embodiment, an array structure is created to access the data, asshown below:

struct { int m_min2; int m_max2; int m_total; char * Glk; }G_info[N_VU_MAX][N_VU_MAX];

The C-matrix data can then be retrieved by utilizing the followingexemplary algorithm:

m_(min2) = G_info[l][k].m_min2 m_(max2) = G_info[l][k].m_max2 N_(g) =L_(g)/N_(c) N1 = m'*N − L_(g)/(2N_(c)) for m' = 0:1 for q = 0:L−1 for q'= 0:L−1 τ = m'T + τ_(lq) − τ_(kq') m_(min1) = N1 − n_(lq) + n_(kq')m_(max1) = m_(min1) + N_(g) m_(min) = max[m_(min1) , m_(min2)] m_(max) =min[m_(max1) , m_(max2)] if m_(max) >= m_(min) m_(span) = m_(max) −m_(min) + 1 sum1 = 0.0; ptr1 = &G_info[l][k].Glk[m_(min)] ptr2 =&g[m_(min) * N_(c) + τ] while m_(span) > 0 sum1 += (*ptr1++) * (*ptr2++)m_(span)−− end C[m'][l][k][q][q'] = sum1 end end end end

A direct method for calculating the C-matrix (in symmetry) isperformance of the following equation:

${C_{k\; l\; q^{\prime}q}\left\lbrack m^{\prime} \right\rbrack} = {\frac{N_{l}}{N_{k}}{C_{l\; k\; q\; q^{\prime}}^{*}\left\lbrack m^{\prime} \right\rbrack}}$

Due to symmetry, there are 1.5(K_(V)L)² elements to calculate. Assumingall users are at SF 256, each calculation requires 256 cmacs, or 2048operations. The probability that a multipath changes in a 10 ms timeperiod is approximately 10/200=0.05 if all users are at 120 kmph.Assuming a mix of user velocities, a reasonable probability is 0.025.Because the C-matrix represents the interaction between two users, theprobability that C-matrix elements change in a 10 ms time period isapproximately 0.10 for all users at 120 kmph, or 0.05 for a mix of usersvelocities. Hence, the GOPS are shown in the following table.

High velocity K_(V) users 1.5(K_(V)L)2 Gops Percentage change GOPS 200100% 960,000 1.966 20 39.3 200  50% 960,000 1.966 15 29.5 128 100%393,216 0.805 20 16.1 128  50% 393,216 0.805 15 12.1

One skilled in the art can appreciate that a fast fourier transform(FFT) can be used to calculate the correlations for a range of offsets,tau, using:

$\begin{matrix}{{C_{k\; l\; q^{\prime}q}\left\lbrack m^{\prime} \right\rbrack} = {\frac{1}{2N_{l}}{\sum\limits_{n}{{s_{k}\left\lbrack {{n\; N_{c}} + {m^{\prime}T} + {\hat{\tau}}_{l\; q} - {\hat{\tau}}_{l\; q^{\prime}}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \\{\;{= {C_{l\; k}\left\lbrack {\tau_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack} \right\rbrack}}} \\{{C_{l\; k}\lbrack\tau\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{s_{k}\left\lbrack {{n\; N_{c}} + \tau} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \\{{\tau_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack} = {{m^{\prime}T} + {\hat{\tau}}_{l\; q} - {\hat{\tau}}_{l\; q^{\prime}}}}\end{matrix}\quad$

The length of the waveform sk[t] is Lg+255N_(C)=1068 for L_(g)=48 andN_(C)=4. This is represented as N_(C) waveforms of lengthL_(g)/N_(C)+255=267. One advantage of this approach is that elements canbe stored for a range of offsets tau so that calculations do not need tobe performed when lags change. For delay spreads of about 4micro-seconds 32 samples need to be stored for each m′.

The C-matrix elements need be updated when the spreading factor changes.The spreading factor can change du to AMR codec rate changes,multiplexing of the dedicated channels, or multiplexing of dataservices, to name a few reasons. It is reasonable to assume that 5% ofthe users, hence 10% of the elements, change every 10 ms.

Gamma-Matrix Generated in FPGA

The C-matrix elements can be represented in terms of the underlying codecorrelations using:

$\begin{matrix}{{C_{k\; l\; q^{\prime}q}\left\lbrack m^{\prime} \right\rbrack} = {\frac{1}{2N_{l}}{\sum\limits_{n}{{s_{k}\left\lbrack {{n\; N_{c}} + {m^{\prime}T} + {\hat{\tau}}_{l\; q} - {\hat{\tau}}_{l\; q^{\prime}}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \\{\;{= {\sum\limits_{m}{{g\left\lbrack {{m\; N_{c}} + \tau} \right\rbrack} \cdot {\Gamma_{l\; k}\lbrack m\rbrack}}}}} \\{{\Gamma_{l\; k}\lbrack m\rbrack} = {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}} \\{\tau \equiv {{m^{\prime}T} + {\hat{\tau}}_{l\; q} - {\hat{\tau}}_{l\; q^{\prime}}}}\end{matrix}\quad$

If the length of g[t] is Lg=48 and Nc=4, then the summation over inrequires 48/4=12 macs for the real part and 12 macs for the imaginarypart. The total ops is then 48 ops per element. (Compare with 2048operations for the direct method.) Hence for the case where there are200 virtual users and 20% of the C-matrix needs updating every 10 ms therequired complexity is (960000 cl)(48 ops/cl)(0.20)/(0.010 sec)=921.6MOPS. This is the required complexity to compute the C-matrix from theTau-matrix. The cost of computing the Tau-matrix must also beconsidered. The Tau-matrix can be efficiently computed since thefundamental operation is a convolution of codes with elementsconstrained to be +/−1+/−j. Further, the Taumatrix can be calculatedusing modulo-2 addition (e.g., XOR) using several method, e.g. registershifting, XOR logic gates, and so on.

The Gamma matrix (Γ) represents the correlation between the complex usercodes. The complex code for user 1 is assumed to be infinite in length,but with only N₁ non-zero values. The non-zero values are constrained tobe ±1±j. The r-matrix can be represented in terms of the real andimaginary parts of the complex user codes, and is based on therelationship:

${\Gamma_{l\; k}^{X\; Y}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}\left\{ {{M_{l\; k}^{X\; Y}\lbrack m\rbrack} - {2{N_{l\; k}^{X\; Y}\lbrack m\rbrack}}} \right\}}$${M_{l\; k}^{X\; Y}\lbrack m\rbrack} \equiv {\sum\limits_{n}{{\cdot {m_{l}^{X}\lbrack n\rbrack}} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}$${N_{l\; k}^{X\; Y}\lbrack m\rbrack} \equiv {\sum\limits_{n}{\left( {{\gamma_{l}^{X}\lbrack n\rbrack} \oplus {\gamma_{k}^{Y}\left\lbrack {n - m} \right\rbrack}} \right) \cdot {m_{l}^{X}\lbrack n\rbrack} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}$

which can be performed using a dual-set of shift registers and a logicalcircuit containing modulo-2 (e.g., Exclusive-OR “XOR”) logic elements.Further, one skilled in the art can appreciate that such a logic devicecan be implemented in a field programmable gate array, which can beprogrammed via the host controller, a compute element, or other deviceincluding an application specific integrated circuit. Further, the FPGAcan be programmed via the RACEway™ bus, for example.

The above shift registers together with a summation device calculatesthe functions M_(lk) ^(XY)[m] and N_(lk) ^(XY)[m]. The remainingcalculations to form Γ_(lk) ^(XY)[m] and subsequently Γ_(lk)[m] can beperformed in software. Note that the four functions Γ_(lk) ^(XY)[m]corrsponding to X, Y=R, I which are components of can be calculated inparallel. For K_(v)=200 virtual users, and assuming that 10% of all (l,k) pairs must be calculated in 2 ms, then for real-time operation wemust calculate 0.10(200)²=4000 elements (all shifts) in 2 ms, or about2M elements (all shifts) per second. For K_(v)=128 virtual users therequirement drops to 0.8192M elements (all shifts) per second.

In what has been presented the elements are calculated for all 512shifts. Not all of these shifts are needed, so it is possible to reducethe number of calculations per elements. The cost is increased designcomplexity.

Therefore, a possible loading scenario for performing short-codemultiple user detection on the hardware described herein is illustratedin FIG. 11. A processor board 118 with four compute elements 220 can beused as shown. Three of the compute nodes (e.g., 220 a–220 c) can beused to calculate the C-matrix and R-matrix. One of the compute nodes(e.g., 220 d) can be used for multiple-stage decision-feedbackinterference cancellation (MDFIC) techniques. The Tau-Matrix andR-Matrix is calculated using FPGA's that can be programmed by the hostcontroller 203, or ASICs. Further, multiuser amplitude estimation isperformed within the modem card 112.

Long-Code Processing

Therefore it can be appreciated by one skilled in the art thatshort-code MUD can be performed using the system architecture describedherein. FIG. 12 shows a preferred embodiment for long-code MUDprocessing. In this embodiment, each frame of data is processed threetimes by the MUD processor, although it can be recognized that multipleprocessors can perform the iterative nature of the embodiment. Duringthe first pass, only the control channels are respread which the maximumratio combination (MRC) and MUD processing is performed on the datachannels. During subsequent passes, data channels are processedexclusively. New y (i.e., soft decisions) and b (i.e., hard decisions)data are derived as shown in the diagram.

Amplitude ratios and amplitudes are determined via the DSP (e.g.,element 900, or a DSP otherwise coupled with the processor board 118 andreceiver 110), as well as certain waveform statistics. These values(e.g., matrices and vectors) are used by the MUD processor in variousways. The MUD processor is decomposed into four stages that closelymatch the structure of the software simulation: Alpha Calculation andRespread 1302, raised-cosine filtering 1304, de-spreading 1306, and MRC1308. Each pass through the MUD processor is equivalent to oneprocessing stage of the software implementation. The design is pipelinedand “parallelized.” In the illustrated embodiment, the clock speed canbe 132 MHz resulting in a throughput of 2.33 ms/frame, however, theclock rate and throughput varies depending on the requirements. Theillustrated embodiment allows for three-pass MUD processing withadditional overhead from external processing, resulting in a 4-timesreal-time processing throughput.

The alpha calculation and respread operations 1302 are carried out by aset of thirty-two processing elements arranged in parallel. These can beprocessing elements within an ASIC, FPGA, PLD or other such device, forexample. Each processing element processes two users of four fingerseach. Values for b are stored in a double-buffered lookup table. Valuesof a(hat) and ja(hat) are pre-multiplied with beta by an externalprocessor and stored in a quad-buffered lookup table. The alphacalculation state generated the following values for each finger, wheresubscripts indicate antenna identifier:α₀=β₀·(C·â ₀ −jC·jâ ₀)jα ₀=β₀·(jC·â ₀ +C·jâ ₀)α1=β₁·(C·â ₁ −jC·jâ ₁)jα ₁=β₁·(jC·â ₁ +C·jâ ₁)

These values are accumulated during the serial processing cycle intofour independent 8-times oversampling buffers. There are eight memoryelements in each buffer and the element used is determined by thesub-chip delay setting for each finger.

Once eight fingers have been accumulated into the oversampling buffer,the data is passed into set of four independent adder-trees. Theseadder-trees each termination in a single output, completing the respreadoperation.

The four raised-cosine filters 1304 convolve the alpha data with a setof weights determined by the following equation:

${g_{i\; c}(t)} = \frac{{\sin\left( {\pi\;\frac{1}{t}} \right)} \cdot {\cos\left( {{\alpha\pi}\;\frac{1}{T}} \right)}}{\pi\;\frac{1}{t}\left( {1 - \left( {2\alpha\;\frac{1}{T}} \right)^{2}} \right)}$

The filters can be implemented with 97 taps with odd symmetry. Thefilters illustrated run at 8-times the chip rate, however, other ratesare possible. The filters can be implemented in a variety of computeelements 220, or other devices such as ASICs, FPGAs for example.

The despread function 1306 can be performed by a set of thirty-twoprocessing elements arranged in parallel. Each processing elementserially processes two users of four fingers each.

For each finger, one chip value out of eight, selected based on thesub-chip delay, is accepted from the output of the raised-cosine filter.The despread state performs the following calculations for each finger(subscripts indicate antenna):

$y_{0} = {{\sum\limits_{0}^{{S\; F} - 1}{C \cdot r_{0}}} + {j\;{C \cdot j}\; r_{0}}}$${j\; y_{0}} = {{\sum\limits_{0}^{{S\; F} - 1}{{C \cdot j}\; r_{0}}} - {j\;{C \cdot \; r_{0}}}}$$y_{1} = {{\sum\limits_{0}^{{S\; F} - 1}{C \cdot r_{1}}} + {j\;{C \cdot j}\; r_{1}}}$${j\; y_{1}} = {{\sum\limits_{0}^{{S\; F} - 1}{{C \cdot j}\; r_{1}}} - {j\;{C \cdot \; r_{1}}}}$

The MRC operations are carried out by a set of four processing elementsarranged in parallel, such as the compute elements 220 for example. Eachprocessor is capable of serially processing eight users of four fingerseach. Values for y are stored in a double-buffered lookup table. Valuesfor b are derived from the MSB of the y data. Note that the b data usedin the MUD stage is independent of the b data used in the respreadstage. Values of â and jâ<are pre-multiplied with β by an externalprocessor and stored in a quad-buffered lookup table. Also, Σ(â²+jâ²)for each channel is stored in a quad-buffered table.

The output stage contains a set of sequential destination bufferpointers for each channel. The data generated by each channel, on a slotbasis, is transferred to the RACEway™ destination indicated by thesebuffers. The first word of each of these transfers will contain acounter in the lower sixteen bits indicating how many y values weregenerated. The upper sixteen bits will contain the constant value0xAA55. This will allow the DSP to avoid interrupts by scanning thefirst word of each buffer.

In addition, the DSP_UPDATE register contains a pointer to singleRACEway™ location. Each time a slot or channel data is transmitted, aninternal counter is written to this location. The counter is limited to10 bits and will wrap around with a terminal count value of 1023.

The method of operation for the long-code multiple user detectionalgorithm (LCMUD) is as follows. Spread factor for four-channelsrequires significant amount of data transfer. In order to limit the gatecount of the hardware implementation, processing an SF4 channel canresult in reduced capability.

A SF4 user can be processed on certain hardware channels. When one ofthese special channels is operating on an SF4 user, the next threechannels are disabled and are therefore unavailable for processing. Thisrelationship is as shown in the following table:

SF4 Chan Disabled Channels 0 1, 2, 3 4 5, 6, 7 8 9, 10, 11 12 12, 14, 1516 17, 18, 19 20 21, 22, 23 24 25, 26, 27 28 29, 30, 31 32 33, 34, 35 3637, 38, 39 40 41, 42, 43 44 45, 46, 47 48 49, 50, 51 52 53, 54, 55 5657, 58, 59 60 61, 62, 63

The default y and b data buffers do not contain enough space for SF4data. When a channel is operating on SF4 data, the y and b buffersextend into the space of the next channel in sequence. For example, ifchannel 0 is processing SF data, the channel 0 and channel 1 b buffersare merged into a single large buffer of 0x40 32-bit words. The ybuffers are merged similarly.

In typical operation, the first pass of the LCMUD algorithm willrespread the control channels in order to remove control interference.For this pass, the b data for the control channels should be loaded intoBLUT while the y data for data channels should be loaded into YDEC. Eachchannel should be configured to operate at the spread factor of the datachannel stored into the YDEC table.

Control channels are always operated at SF 256, so it is likely that thecontrol data will need to be replicated to match the data channel spreadfactor. For example, each bit (b entry) of control data would bereplicated 64 times if that control channel were associated with an SF 4data channel.

Each finger in a channel arrives at the receiver with a different delay.During the Respread operation, this skew among the fingers is recreated.During the MRC stage of MUD processing, it is necessary to remove thisskew and realign the fingers of each channel.

This is accomplished in the MUD processor by determining the first bitavailable from the most delayed finger and discarding all previous bitsfrom all other fingers. The number of bits to discard can beindividually programmed for each finger with the Discard field of theMUDPARAM registers.

This operation will typically result in a ‘short’ first slot of data.This is unavoidable when the MUD processor is first initialized andshould not create any significant problems. The entire first slot ofdata can be completely discarded if ‘short’ slots are undesirable.

A similar situation will arise each time processing is begun on a frameof data. To avoid losing data, it is recommended that a partial slot ofdata from the previous frame be overlapped with the new frame. Trimmingany redundant bits created this way can be accomplished with the Discardregister setting or in the system DSP. In order to limit memoryrequirements, the LCMUD FPGA processes one slot of data at a time.Doubling buffering is used for b and y data so that processing cancontinue as data is streamed in. Filling these buffers is complicated bythe skew that exists among fingers in a channel.

FIG. 13 illustrates the skew relationship among fingers in a channel andamong the channels themselves. The illustrated embodiment allows for 20us (77.8 chips) of skew among fingers in a channel and certain skewamong channels, however, in other embodiments these skew allowancesvary.

There are three related problems that are introduced by skew:Identifying frame & slot boundaries, populating b and y tables andchanging channel constants.

Because every finger of every channel can arrive at a different time,there are no universal frame and slot boundaries. The DSP must select anarbitrary reference point. The data stored in b & y tables is likely tocome from two adjacent slots.

Because skew exists among fingers in a channel, it is not enough topopulate the b & y tables with 2,560 sequential chips of data. Theremust be some data overlap between buffers to allow lagging channels toaccess “old”data. The amount of overlap can be calculated dynamically orfixed at some number greater than 78 and divisible by four (e.g. 80chips). The starting point for each register is determined by the ChipAdvance field of the MUDPARAM register.

A related problem is created by the significant skew among channels. Ascan be seen in FIG. 13, Channel 0 is receiving Slot 0 while Channel 1 isreceiving Slot 2. The DSP must take this skew into account whengenerating the b and y tables and temporally align channel data.

Selecting an arbitrary “slot” of data from a channel implies thatchannel constants tied to the physical slot boundaries may change whileprocessing the arbitrary slot. The Constant Advance field of theMUDPARAM register is used to indicate when these constants shouldchange.

Registers affected this way are quad-buffered. Before data processingbegins, at least two of these buffers should be initialized. Duringnormal operation, one additional buffer is initialized for each slotprocessed. This system guarantees that valid constants data will alwaysbe available.

The following two tables shown the long-code MUD FPGA memory map andcontrol/status register:

Start Addr End Addr Name Description 0000_0000 0000_0000 CSR Control &Status Register 0000_0008 0000_000C DSP_UPDATE Route & Address for DSPupdating 0001_0000 0001_FFFF MUDPARAM MUD Parameters 0002_0000 0002_FFFFCODE Spreading Codes 0003_0000 0004_FFFF BLUT Respread: b Lookup Table0005_0000 0005_FFFF BETA_A Respread: Beta * a_hat Lookup Table 0006_00000007_FFFF YDEC MUD & MRC: y Lookup Table 0008_0000 0008_FFFF ASQ MUD &MRC: Sum a_hat squared LUT 000A_0000 000A_FFFF OUTPUT Output Routes &Addresses

Bit 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 Name Reserved R/W ROReset X X X X X X X X X X X X X X X X Bit 15 14 13 12 11 10 9 8 7 6 5 43 2 1 0 Name Reserved YB CBUF A1 A0 R1 R0 Lst Rst R/W RO RO RO RO RO RwRw Rw Rw Reset X X X X X X X 0 0 0 0 0 0 0 0 0

The register YB indicates which of two y and b buffers are in use. Ifthe system is currently not processing, YB indicates the buffer thatwill be used when processing is initiated.

CBUF indicates which of four round-robin buffers for MUD constants (a^beta) is currently in use. Finger skew will result in some fingers usinga buffer one in advance of this indicator. To guarantee that valid datais always available, two full buffers should be initialized beforeoperation begins.

If the system is currently not processing, CBUF indicates the bufferthat will be used when processing is restarted. It is technicallypossible to indicate precisely which buffer is in use for each finger inboth the Respread and Despread processing stages. However, this wouldrequire thirty-two 32-bit registers. Implementing these registers wouldbe costly, and the information is of little value.

A1 and A0 indicate which y and b buffers are currently being processed.A1 and A0 will never indicate ‘1’ at the same time. An indication of ‘0’for both A1 and A0 means that MUD processor is idle.

R1 and R0 are writable fields that indicate to the MUD processor thatdata is available. R1 corresponds to y and b buffer 1 and R0 correspondsto y and b buffer 0. Writing a ‘1’ into the correct register willinitiate MUD processing. Note that these buffers follow strictround-robin ordering. The YB register indicates which buffer should beactivated next.

These registers will be automatically reset to ‘0’ by the MUD hardwareonce processing is completed. It is not possible for the externalprocessor to force a ‘0’ into these registers.

A ‘1’ in this bit indicates that this is the last slot of data in aframe. Once all available data for the slot has been processed, theoutput buffers will be flushed.

A ‘1’ in this bit will place the MUD processor into a reset state. Theexternal processor must manually bring the MUD processor out of reset bywriting a ‘0’ into this bit.

DSP_UPDATE is arranged as two 32-bit registers. A RACEway™ route to theMUD DSP is stored at address 0x0000_(—)0008. A pointer to a statusmemory buffer is located at address 0x0000_(—)000C.

Each time the MUD processor writes a slot of channel data to acompletion buffer, an incrementing count value is written to thisaddress. The counter is fixed at 10 bits and will wrap around after aterminal count of 1023.

A quad-buffered version of the MUD parameter control register exists foreach finger to be processed. Execution begins with buffer 0 andcontinues in round-robin fashion. These buffers are used insynchronization with the MUD constants (Beta * a_hat, etc.) buffers.Each finger is provided with an independent register to allowindependent switching of constant values at slot and frame boundaries.The following table shows offsets for each MUD channel:

Offset User 0x0000 0 0x0040 1 0x0080 2 0x00C0 3 0x0100 4 0x0140 5 0x01806 0x01C0 7 0x0200 8 0x0240 9 0x0280 10 0x02C0 11 0x0300 12 0x0340 130x0380 14 0x03C0 15 0x0400 16 0x0440 17 0x0480 18 0x04C0 19 0x0500 200x0540 21 0x0580 22 0x05C0 23 0x0600 24 0x0640 25 0x0680 26 0x06C0 270x0700 28 0x0740 29 0x0780 30 0x07C0 31 0x0800 32 0x0840 33 0x0880 340x08C0 35 0x0900 36 0x0940 37 0x0980 38 0x09C0 39 0x0A00 40 0x0A40 410x0A80 42 0x0AC0 43 0x0B00 44 0x0B40 45 0x0B80 46 0x0BC0 47 0x0C00 480x0C40 49 0x0C80 50 0x0CC0 51 0x0D00 52 0x0D40 53 0x0D80 54 0x0DC0 550x0E00 56 0x0E40 57 0x0E80 58 0x0EC0 59 0x0F00 60 0x0F40 61 0x0F80 620x0FC0 63

The following table shows buffer offsets within each channel:

Offset Finger Buffer 0x0000 0 0 0x0004 1 0x0008 2 0x000C 3 0x0010 1 00x0014 1 0x0018 2 0x001C 3 0x0020 2 0 0x0024 1 0x0028 2 0x002C 3 0x00303 0 0x0034 1 0x0038 2 0x003C 3

The following table shown details of the control register:

Bit 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 Name Spread FactorSubchip Delay Discard R/W RW RW RW Reset X X X X X X X X X X X X X X X XBit 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Name Chip Advance ConstantAdvance R/W RW RW Reset X X X X X X X X X X X X X X X X

The spread factor field determines how many chip samples are used togenerate a data bit. In the illustrated embodiment, all fingers in achannel have the same spread factor setting, however, it can beappreciated by one skilled in the art that such constant factor settingcan be variable in other embodiments. The spread factor is encoded intoa 3-bit value as shown in the following table:

SF Factor Spread Factor 000 256 001 128 010 64 011 32 100 16 101 8 110 4111 RESERVED

The field specifics the sub-chip delay for the finger. It is used toselect one of eight accumulation buffers prior to summing all Alphavalues and passing them into the raised-cosine filter.

Discard determines how many MUD-processed soft decisions (y values) todiscard at the start of processing. This is done so that the first yvalue from each finger corresponds to the same bit. After the first slotof data is processed, the Discard field should be set to zero.

The behavior of the discard field is different than that of otherregister fields. Once a non-zero discard setting is detected, any newdiscard settings from switching to a new table entry are ignored untilthe current discard count reaches zero. After the count reaches zero, anew discard setting may be loaded the next time a new table entry isaccessed.

All fingers within a channel will arrive at the receiver with differentdelays. Chip Advance is used to recreate this signal skew during theRespread operation. Y and b buffers are arranged with older dataoccupying lower memory addresses. Therefore, the finger with theearliest arrival time has the highest value of chip advance. ChipAdvanced need not be a multiple of Spread Factor.

Constant advance indicates on which chip this finger should switch to anew set of constants (e.g. a^) and a new control register setting. Notethat the new values take effect on the chip after the value stored here.For example, a value of 0x0 would cause the new constants to take effecton chip 1. A value of 0xFF would cause the new constants to take effecton chip 0 of the next slot. The b lookup tables are arranged as shown inthe following table. B values each occupy two bits of memory, althoughonly the LSB is utilized by LCMUD hardware.

Offset Buffer 0x0000 U0 B0 0x0020 U1 B0 0x0040 U0 B1 0x0060 U1 B1 0x0080U2 B0 0x00A0 U3 B0 0x00C0 U2 B1 0x00E0 U3 B1 0x0100 U4 B0 0x0120 U5 B00x0140 U4 B1 0x0160 U5 B1 0x0180 U6 B0 0x01A0 U7 B0 0x01C0 U6 B1 0x01E0U7 B1 0x0200 U8 B0 0x0220 U9 B0 0x0240 U8 B1 0x0260 U9 B1 0x0280 U10 B00x02A0 U11 B0 0x02C0 U10 B1 0x02E0 U11 B1 0x0300 U12 B0 0x0320 U13 B00x0340 U12 B1 0x0360 U13 B1 0x0380 U14 B0 0x03A0 U15 B0 0x03C0 U14 B10x03E0 U15 B1 0x0400 U16 B0 0x0420 U17 B0 0x0440 U16 B1 0x0460 U17 B10x0480 U18 B0 0x04A0 U19 B0 0x04C0 U18 B1 0x04E0 U19 B1 0x0500 U20 B00x0520 U21 B0 0x0540 U20 B1 0x0560 U21 B1 0x0580 U22 B0 0x05A0 U23 B00x05C0 U22 B1 0x05E0 U23 B1 0x0600 U24 B0 0x0620 U25 B0 0x0640 U24 B10x0660 U25 B1 0x0680 U26 B0 0x06A0 U27 B0 0x06C0 U26 B1 0x06E0 U27 B10x0700 U28 B0 0x0720 U29 B0 0x0740 U28 B1 0x0760 U29 B1 0x0780 U30 B00x07A0 U31 B0 0x07C0 U30 B1 0x07E0 U31 B1 0x0800 U32 B0 0x0820 U33 B00x0840 U32 B1 0x0860 U33 B1 0x0880 U34 B0 0x08A0 U35 B0 0x08C0 U34 B10x08E0 U35 B1 0x0900 U36 B0 0x0920 U37 B0 0x0940 U36 B1 0x0960 U37 B10x0980 U38 B0 0x09A0 U39 B0 0x09C0 U38 B1 0x09E0 U39 B1 0x0A00 U40 B00x0A20 U41 B0 0x0A40 U40 B1 0x0A60 U41 B1 0x0A80 U42 B0 0x0AA0 U43 B00x0AC0 U42 B1 0x0AE0 U43 B1 0x0B00 U44 B0 0x0B20 U45 B0 0x0B40 U44 B10x0B60 U45 B1 0x0B80 U46 B0 0x0BA0 U47 B0 0x0BC0 U46 B1 0x0BE0 U47 B10x0C00 U48 B0 0x0C20 U49 B0 0x0C40 U48 B1 0x0C60 U49 B1 0x0C80 U50 B00x0CA0 U51 B0 0x0CC0 U50 B1 0x0CE0 U51 B1 0x0D00 U52 B0 0x0D20 U53 B00x0D40 U52 B1 0x0D60 U53 B1 0x0D80 U54 B0 0x0DA0 U55 B0 0x0DC0 U54 B10x0DE0 U55 B1 0x0E00 U56 B0 0x0E20 U57 B0 0x0E40 U56 B1 0x0E60 U57 B10x0E80 U58 B0 0x0EA0 U59 B0 0x0EC0 U58 B1 0x0EE0 U59 B1 0x0F00 U60 B00x0F20 U61 B0 0x0F40 U60 B1 0x0F60 U61 B1 0x0F80 U62 B0 0x0FA0 U63 B00x0FC0 U62 B1 0x0FE0 U63 B1

The following table illustrates how the two-bit values are packed into32-bit words. Spread Factor 4 channels require more storage space thanis available in a single channel buffer. To allow for SF4 processing,the buffers for an even channel and the next highest odd channel arejoined together. The even channel performs the processing while the oddchannel is disabled.

Bit 31 30 29 28 27 26 25 24 23 22 21 20 19 18 17 16 Name b(0) b(1) b(2)b(3) b(4) b(5) b(6) b(7) Bit 15 14 13 12 11 10 9 8 7 6 5 4 3 2 1 0 Nameb(8) b(9) b(10) b(11) b(12) b(13) b(14) b(15)

The beta*a-hat table contains the amplitude estimates for each fingerpre-multiplied by the value of Beta. The following table shows thememory mappings for each channel.

Offset User 0x0000 0 0x0080 1 0x0100 2 0x0180 3 0x0200 4 0x0280 5 0x03006 0x0380 7 0x0400 8 0x0480 9 0x0500 10 0x0580 11 0x0600 12 0x0680 130x0700 14 0x0780 15 0x0800 16 0x0880 17 0x0900 18 0x0980 19 0x0A00 200x0A80 21 0x0B00 22 0x0B80 23 0x0C00 24 0x0C80 25 0x0D00 26 0x0D80 270x0E00 28 0x0E80 29 0x0F00 30 0x0F80 31 0x1000 32 0x1080 33 0x1100 340x1180 35 0x1200 36 0x1280 37 0x1300 38 0x1380 39 0x1400 40 0x1480 410x1500 42 0x1580 43 0x1600 44 0x1680 45 0x1700 46 0x1780 47 0x1800 480x1880 49 0x1900 50 0x1980 51 0x1A00 52 0x1A80 53 0x1B00 54 0x1B80 550x1C00 56 0x1C80 57 0x1D00 58 0x1D80 59 0x1E00 60 0x1E80 61 0x1F00 620x1F80 63

The following table shows buffers that are distributed for each channel:

Offset User Buffer 0x00 0 0x20 1 0x40 2 0x80 3The following table shows a memory mapping for individual fingers ofeach antenna.

Offset Finger Antenna 0x00 0 0 0x04 1 0x08 2 0x0C 3 0x10 0 1 0x14 1 0x182 0x1C 3

The y (soft decisions) table contains two buffers for each channel. Likethe b lookup table, an even and odd channel are bonded together toprocess SF4. Each y data value is stored as a byte. The data is writteninto the buffers as packed 32-bit words.

Offset Buffer 0x0000 U0 B0 0x0200 U1 B0 0x0400 U2 B1 0x0600 U3 B1 0x0800U0 B0 0x0A00 U1 B0 0x0C00 U2 B1 0x0E00 U3 B1 0x0000 U4 B0 0x0200 U5 B00x0400 U6 B1 0x0600 U7 B1 0x0800 U4 B0 0x0A00 U5 B0 0x0C00 U6 B1 0x0E00U7 B1 0x0000 U8 B0 0x0200 U9 B0 0x0400 U10 B1 0x0600 U11 B1 0x0800 U8 B00x0A00 U9 B0 0x0C00 U10 B1 0x0E00 U11 B1 0x0000 U12 B0 0x0200 U13 B00x0400 U14 B1 0x0600 U15 B1 0x0800 U12 B0 0x0A00 U13 B0 0x0C00 U14 B10x0E00 U15 B1 0x4000 U16 B0 0x4200 U17 B0 0x4400 U18 B1 0x4600 U19 B10x4800 U16 B0 0x4A00 U17 B0 0x4C00 U18 B1 0x4E00 U19 B1 0x5000 U20 B00x5200 U21 B0 0x5400 U22 B1 0x5600 U23 B1 0x5800 U20 B0 0x5A00 U21 B00x5C00 U22 B1 0x5E00 U23 B1 0x6000 U24 B0 0x6200 U25 B0 0x6400 U26 B10x6600 U27 B1 0x6800 U24 B0 0x6A00 U25 B0 0x6C00 U26 B1 0x6E00 U27 B10x7000 U28 B0 0x7200 U29 B0 0x7400 U30 B1 0x7600 U31 B1 0x7800 U28 B00x7A00 U29 B0 0x7C00 U30 B1 0x7E00 U31 B1 0x8000 U32 B0 0x8200 U33 B00x8400 U34 B1 0x8600 U35 B1 0x8800 U32 B0 0x8A00 U33 B0 0x8C00 U34 B10x8E00 U35 B1 0x9000 U36 B0 0x9200 U37 B0 0x9400 U38 B1 0x9600 U39 B10x9800 U36 B0 0x9A00 U37 B0 0x9C00 U38 B1 0x9E00 U39 B1 0xA000 U40 B00xA200 U41 B0 0xA400 U42 B1 0xA600 U43 B1 0xA800 U40 B0 0xAA00 U41 B00xAC00 U42 B1 0xAE00 U43 B1 0xB000 U44 B0 0xB200 U45 B0 0xB400 U46 B10xB600 U47 B1 0xB800 U44 B0 0xBA00 U45 B0 0xBC00 U46 B1 0xBE00 U47 B10xC000 U48 B0 0xC200 U49 B0 0xC400 U50 B1 0xC600 U51 B1 0xC800 U48 B00xCA00 U49 B0 0xCC00 U50 B1 0xCE00 U51 B1 0xD000 U52 B0 0xD200 U53 B00xD400 U54 B1 0xD600 U55 B1 0xD800 U52 B0 0xDA00 U53 B0 0xDC00 U54 B10xDE00 U55 B1 0xE000 U56 B0 0xE200 U57 B0 0xE400 U58 B1 0xE600 U59 B10xE800 U56 B0 0xEA00 U57 B0 0xEC00 U58 B1 0xEE00 U59 B1 0xF000 U60 B00xF200 U61 B0 0xF400 U62 B1 0xF600 U63 B1 0xF800 U60 B0 0xFA00 U61 B00xFC00 U62 B1 0xFE00 U63 B1

The sum of the a-hat squares is stored as a 16-bit value. The followingtable contains a memory address mapping for each channel.

Offset User 0x0000 0 0x0020 1 0x0040 2 0x0060 3 0x0080 4 0x00A0 5 0x00C06 0x00E0 7 0x0100 8 0x0120 9 0x0140 10 0x0160 11 0x0180 12 0x01A0 130x01C0 14 0x01E0 15 0x0200 16 0x0220 17 0x0240 18 0x0260 19 0x0280 200x02A0 21 0x02C0 22 0x02E0 23 0x0300 24 0x0320 25 0x0340 26 0x0360 270x0380 28 0x03A0 29 0x03C0 30 0x03E0 31 0x0400 32 0x0420 33 0x0440 340x0460 35 0x0480 36 0x04A0 37 0x04C0 38 0x04E0 39 0x0500 40 0x0520 410x0540 42 0x0560 43 0x0580 44 0x05A0 45 0x05C0 46 0x05E0 47 0x0600 480x0620 49 0x0640 50 0x0660 51 0x0680 52 0x06A0 53 0x06C0 54 0x06E0 550x0700 56 0x0720 57 0x0740 58 0x0760 59 0x0780 60 0x07A0 61 0x07C0 620x07E0 63

Within each buffer, the value for antenna 0 is stored at address offset0x0 with the value for antenna one stored at address offset 0x04. Thefollowing table demonstrates a mapping for each finger.

Offset User Buffer 0x00 0 0x08 1 0x10 2 0x1C 3

Each channel is provided a RACEway™ route on the bus, and a base addressfor buffering output on a slot basis. Registers for controlling buffersare allocated as shown in the following two tables. External devices areblocked from writing to register addresses marked as reserved.

Offset User 0x0000 0 0x0020 1 0x0040 2 0x0060 3 0x0080 4 0x00A0 5 0x00C06 0x00E0 7 0x0100 8 0x0120 9 0x0140 10 0x0160 11 0x0180 12 0x01A0 130x01C0 14 0x01E0 15 0x0200 16 0x0220 17 0x0240 18 0x0260 19 0x0280 200x02A0 21 0x02C0 22 0x02E0 23 0x0300 24 0x0320 25 0x0340 26 0x0360 270x0380 28 0x03A0 29 0x03C0 30 0x03E0 31 0x0400 32 0x0420 33 0x0440 340x0460 35 0x0480 36 0x04A0 37 0x04C0 38 0x04E0 39 0x0500 40 0x0520 410x0540 42 0x0560 43 0x0580 44 0x05A0 45 0x05C0 46 0x05E0 47 0x0600 480x0620 49 0x0640 50 0x0660 51 0x0680 52 0x06A0 53 0x06C0 54 0x06E0 550x0700 56 0x0720 57 0x0740 58 0x0760 59 0x0780 60 0x07A0 61 0x07C0 620x07E0 63

Offset Entry 0x0000 Route to Channel Destination 0x0004 Base Address forBuffers 0x0008 Buffers 0x000C RESERVED 0x0010 RESERVED 0x0014 RESERVED0x0018 RESERVED 0x001C RESERVED

Slot buffer size is automatically determined by the channel spreadfactor. Buffers are used in round-robin fashion and all buffers for achannel must be arranged contiguously. The buffers control registerdetermines how many buffers are allocated for each channel. A setting of0 indicates one available buffer, a setting of 1 indicates two availablebuffers, and so on.

Methods for Estimating Symbols Embodied in Short-Code User Wave-Forms

As discussed above, systems according to the invention performmulti-user detection by determining correlations among the userchannel-corrupted waveforms and storing these correlations as elementsof the R-matrices. The correlations are updated in real time to trackcontinually changing channel characteristics. The changes can stein fromchanges in user code correlations, which depend on the relative lagamong various user multi-path components, as well as from the muchfaster variations of the Rayleigh-fading multi-path amplitudes. Therelative lags among multi-path components can change with a timeconstant, for example, of about 400 ms whereas the multi-path amplitudescan vary temporally with a time constant of, for example, 1.33 ms. TheR-matrices are used to cancel the multiple access interference throughthe Multi-stage Decision-Feedback Interference Cancellation (MDFIC)technique.

In the preceding discussion and those that follow, the term physicaluser refers to a CDMA signal source, e.g., a user cellular phone, modemor other CDMA signal source, the transmitted waveforms from which areprocessed by a base station and, more particularly, by MUD processingcard 118. In the illustrated embodiment, each physical user isconsidered to be composed of a one or more virtual users and, moretypically, a plurality of virtual users.

A virtual user is deemed to “transmit” a single bit per symbol period,where a symbol period can be, for example, a time duration of 256 chips( 1/15 ms). Thus, the number of virtual users, for a given physicaluser, is equal to the number of bits transmitted in a symbol period.

In the illustrated embodiment, each physical user is associated with atleast two virtual users, one of which corresponds to a DedicatedPhysical Control Channel (DPCCH) and the other of which corresponds to aDedicated Physical Data Channel (DPDCH). Other embodiments may providefor a single virtual user per physical user, as well, of course, tothree or more virtual users per physical user.

In the illustrated embodiment, when a Spreading Factor (SF) associatedwith a physical user is less than 256, the J=256/SF data bits and onecontrol bit are transmitted per symbol period. Hence, for the r^(th)physical user with data-channel spreading factor SF, ,there are a totalof 1+256/SF, virtual users. The total number of virtual users can thenbe denoted by:

$\begin{matrix}{K_{v} \equiv {\sum\limits_{r = 1}^{K}\left\lbrack {1 + \frac{256}{S\; F_{r}}} \right\rbrack}} & (1)\end{matrix}$

The waveform transmitted by the rth physical user can be written as:

$\begin{matrix}{{{x_{r}\lbrack t\rbrack} = {\sum\limits_{k = 1}^{1 + J_{r}}{\beta_{k}{\sum\limits_{m}{{s_{k}\left\lbrack {t - {m\; T}} \right\rbrack}{b_{k}\lbrack m\rbrack}}}}}}{{s_{k}\lbrack t\rbrack} \equiv {\sum\limits_{p = 0}^{N - 1}{{h\left\lbrack {t - {p\; N_{c}}} \right\rbrack}{c_{k}\lbrack p\rbrack}}}}} & (2)\end{matrix}$

where t is the integer time sample index, T=NN_(c) represents the databit duration, N=256 represents short-code length, N_(c) is the number ofsamples per chip, and where β_(k)=β_(c) if the kth virtual user is acontrol channel and β_(k)=β_(d) if the kth virtual user is a datachannel. The multipliers β_(c) and β_(d) are utilized to select therelative amplitudes of the control and data channels. In the illustratedembodiment, at least one of the above constants equals 1 for any givensymbol period, m.

The waveform sk[t], which is herein referred to as the transmittedsignature waveform for the kth virtual user, is generated by theillustrated system by passing the spread code sequence ck[n] through aroot-raised-cosine pulse shaping filter h[t]. When the kth virtual usercorresponds to a data user with a spreading factor that is less than256, the code ck[n] retains a length of 256, but only Nk of these 256elements are non-zero, where Nk is the spreading factor for the kthvirtual user. The non-zero values are extracted from the codeC_(ch, 256, 64) [n]·s_(sh)[n].

The baseband received signal can be written as:

$\begin{matrix}{{{r\lbrack t\rbrack} = {{\sum\limits_{k = 1}^{K_{r}}{\sum\limits_{m}{{{\overset{\sim}{s}}_{k}\left\lbrack {t - {m\; T}} \right\rbrack}{b_{k}\lbrack m\rbrack}}}} + {w\lbrack t\rbrack}}}{{s_{k}\lbrack t\rbrack} \equiv {\sum\limits_{q^{\prime} = \; 1}^{L}{a_{k\; q}{s_{k}\left\lbrack {t - \tau_{k\; q^{\prime}}} \right\rbrack}}}}} & (3)\end{matrix}$

where w[t] is receiver noise, {tilde over (s)}_(k)[t] is thechannel-corrupted signature waveform for virtual user k, L is the numberof multipath components, and a_(kq′) are the complex multipathamplitudes. The amplitude ratios β_(k) are incorporated into theamplitudes a_(kq′). If k and l are two virtual users that correspond tothe same physical user then, aside from scaling factors β_(k) and β_(p),a_(kq′) and a_(lq′) are equal. This is due to the fact that the signalwaveforms of all virtual users corresponding to the same physical userpass through the same channel. Further, the waveform S_(k)[t] representsthe received signature waveform for the k^(th) virtual user, and itdiffers from the transmitted signature waveform given in Equation (2) inthat the root-raised-cosine pulse h[t] is replaced with theraised-cosine pulse g[t].

The received signal that has been match-filtered to the chip pulse isalso match-filtered in the illustrated embodiment to the user codesequence in order to obtain detection statistic, herein referred to asy_(k), for the k^(th) virtual user. Because there are K_(v) codes, thereare K_(v) such detection statistics. For each virtual user, thedetection statistics can be collected into a column vector y[m] whosem^(th) entry corresponds to the m^(th) symbol period. More particularly,the matched filter output y_(l)[m] for the l^(th) virtual user can bewritten as:

$\begin{matrix}{{y_{l}\lbrack m\rbrack} \equiv {R\; e\left\{ {\sum\limits_{q = 1}^{L}{{{\hat{a}}_{l\; q}^{*} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{{r\left\lbrack {{n\; N_{c}} + {\hat{\tau}}_{l\; q} + {m\; T}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \right\}}} & (4)\end{matrix}$

where â_(lq)* is an estimate of a_(lq)*, {circumflex over (τ)}_(lq) isan estimate of τ_(lq), N_(l) is the (non-zero) length of code c_(l)[n],and η_(l)[m] represents the match-filtered receiver noise. Substitutingthe expression for r[t] from Equation (3) in Equation (4) results in thefollowing equation:

$\begin{matrix}\begin{matrix}{{y_{l}\lbrack m\rbrack} \equiv {\sum\limits_{m^{\prime}}{\sum\limits_{k = 1}^{K_{\gamma}}{R\; e\left\{ {\sum\limits_{q = 1}^{L}{{{\hat{a}}_{l\; q}^{*} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{{\overset{\sim}{s}}_{k}\left\lbrack {{n\; N_{c}} +} \right.}}}} \right.}}}} \\{{\left. {\left. {{\hat{\tau}}_{l\; q} + {m^{\prime}T}} \right\rbrack \cdot {c_{l}^{*}\lbrack n\rbrack}}\; \right\}{b_{k}\left\lbrack {m - m^{\prime}} \right\rbrack}} + {\eta_{l}\lbrack m\rbrack}} \\{= {{\sum\limits_{m^{\prime}}{\sum\limits_{k = 1}^{K_{\gamma}}{{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack}{b_{k}\left\lbrack {m - m^{\prime}} \right\rbrack}}}} + {\eta_{l}\lbrack m\rbrack}}} \\{{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \equiv {R\; e\left\{ {\sum\limits_{q = 1}^{L}{{{\hat{a}}_{l\; q}^{*} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{{{\overset{\sim}{s}}_{k}\left\lbrack {{n\; N_{c}} + {\hat{\tau}}_{l\; q} + {m^{\prime}T}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \right\}}} \\{= {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {{\hat{a}}_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{s_{k}\left\lbrack {{n\; N_{c}} + {m^{\prime}T} +} \right.}}} \right.}}}} \\\left. {{\left. {{\hat{\tau}}_{l\; q} - \tau_{k\; q^{\prime}}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}} \right\} \\{= {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {{\hat{a}}_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{\sum\limits_{p}{g\left\lbrack {{\left( {n - p} \right)N_{c}} + {m^{\prime}T} +} \right.}}}} \right.}}}} \\\left. {{\left. {{\hat{\tau}}_{l\; q} - \tau_{k\; q^{\prime}}} \right\rbrack}{c_{k}\lbrack p\rbrack}{c_{l}^{*}\lbrack n\rbrack}} \right\}\end{matrix} & (5)\end{matrix}$

The terms for m′=0 result from asynchronous users.

Calculation of the R-Matrix

Determination of the R-matrix elements defined by Equation (5) above canbe divided into two or more separate calculations, each having anassociated time constant or period of execution corresponding to a timeconstant or period during which a corresponding characteristic of theuser waveforms are expected to change in real time. In the illustratedembodiment, three sets of calculations are employed as reflected in thefollowing equations:

$\begin{matrix}\begin{matrix}{{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {{a_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{\sum\limits_{p}{g\left\lbrack {\left( {n - p} \right)N_{c}} \right.}}}} + {m^{\prime}T} +} \right.}}}} \\\left. {\left. {\tau_{l\; q} - \tau_{k\; q^{\prime}}} \right\rbrack{c_{k}\lbrack p\rbrack}{c_{l}^{*}\lbrack n\rbrack}} \right\} \\{= {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {a_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot {C_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack}}} \right\}}}}} \\{{C_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack} \equiv {{\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{p}{g\left\lbrack {\left( {n - p} \right)N_{c}} \right.}}}} + {m^{\prime}T} + \tau_{l\; q} - {\tau_{k\; q^{\prime}}\text{]}{{c_{k}\lbrack p\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{m}{{g\left\lbrack {{m\; N_{c}} + {m^{\prime}T} + \tau_{l\; q} - \tau_{k\; q^{\prime}}} \right\rbrack}{\sum\limits_{n}{{c_{k}\left\lbrack {n - m} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{m}{{g\left\lbrack {{m\; N_{c}} + {m^{\prime}T} + \tau_{l\; q} - \tau_{k\; q^{\prime}}} \right\rbrack}{\Gamma_{l\; k}\lbrack m\rbrack}}}}} \\{{\Gamma_{l\; k}\lbrack m\rbrack} \equiv {\sum\limits_{n}{{c_{k}\left\lbrack {n - m} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}\end{matrix} & (6)\end{matrix}$

where the hats (^), indicating parameter estimates, have been omitted.

With reference to Equation (6), the Γ-matrix, whose elements vary withthe slowest time constant, represents the user code correlations for allvalues of offset in. For the case of 100 voice users, the total memoryrequirement for storing the Γ-matrix elements is 21 Mbytes based on twobytes (e.g., the real and imaginary parts) per element. In theillustrated embodiment, the Γ-matrix matrix is updated only when newcodes associated with new users are added to the system. Hence, theΓ-matrix is effectively a quasi-static matrix, and thus, itscomputational requirements are minimal.

The selection of the most efficient method for calculating the Γ-matrixelements depends on the non-zero length of the codes. For example, thenon-zero length of the codes in case of high data-rate users can be only4 chips long. In such a case, a direct convolution, e.g., convolution inthe time domain, can be the most efficient method of calculating theelements of the Γ-matrix. For low data-rate users, it may be moreefficient to calculate the elements of the Γ-matrix by utilizing FastFourier Transforms (FFTs) to perform convolutions in the frequencydomain.

In one method according to the teachings of the invention, the C-matrixelements are calculated by utilizing the Γ-matrix elements. The C-matrixelements need to be calculated upon occurrence of a change in a user'sdelay lag (e.g., time-lag). For example, consider a case in which eachmulti-path component changes on average every 400 ms, and the length ofthe g[ ] function is 48 samples. In such a case, assuming anover-sampling by four, then forty-eight operations per element need tobe performed (for example, 12 multiple accumulations, real x complex,for each element). Further, if 100 low-rate users (i.e., 200 virtualusers) are utilizing the system, and assuming a single multipath lag offour changes for one user, a total of (1.5)(2)K_(v)LN_(v) elements needto be calculated. The factor of 1.5 arises from the three C-matrices(e.g., m′=−1,0,1) which is reduced by a factor two as a result of aconjugate symmetry condition. Moreover, the factor two arises based onthe fact that both rows and columns need to be updated. The factor N_(v)represents the number of virtual users per physical user, which for thelowest rate users is N_(v)=2 as stated above. In total, this amounts toapproximately 230,400 operations per multipath component per physicaluser. Accordingly, it gives rise to 230 MOPS based on 100 physical userswith four multipath components per user, each changing once per 400msec. Of course, in other embodiments these values can differ.

The C-matrices are then utilized to calculate the R-matrices. Moreparticularly, the elements of the R-matrix can be obtained as follows byutilizing Equation (6) above:

$\begin{matrix}{\left. {{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {{\hat{a}}_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot C_{l\; k\; q\; q^{\prime}}}} \middle| m^{\prime} \right\rbrack}}}} \right\} = {R\; e\left\{ {a_{l}^{H} \cdot {C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k}} \right\}}} & (7)\end{matrix}$

where a_(k) are L×l vectors, and C_(lk)[m′] are L×L matrices. The rateat which the above calculations need to be performed depends on thevelocity of the users. For example, in one embodiment, the update rateis selected to be 1.33 msec. An update rate that is too slow such thatthe estimated values of the R-matrix deviate significantly from theactual R-matrix values results in a degradation of the MUD efficiency.For example, FIG. 14 presents a graph that depicts the change in the MUDefficiency versus user velocity for an update rate of 1.33 msec, whichcorresponds to two WCDMA time slots. This graph indicates that the MUDefficiency is high for users having velocities that are less than about100 km/h. The graph further shows that the interference corresponding tofast users is not canceled as effectively as the interferencecorresponding to slow users. Thus, for a system that is utilized by amix of fast and slow users, the total MUD efficiency is an average ofthe MUD efficiency for the range of user velocities. Utilizing the aboveEquation (7), the R-matrix elements can be calculated in terms of an Xmatrix that represents amplitude-amplitude multiplies as shown below:

$\begin{matrix}\begin{matrix}{{r_{l\; k}\left\lbrack m^{\prime} \right\rbrack} = {{R\; e\left\{ {t\;{r\left\lbrack {a_{l}^{H} \cdot {C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k}} \right\rbrack}} \right\}} = {R\; e\left\{ {t\;{r\left\lbrack {{C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k} \cdot a_{l}^{H}} \right\rbrack}} \right\}}}} \\{\equiv {R\; e\left\{ {t\;{r\left\lbrack {{C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot X_{l\; k}} \right\rbrack}} \right\}}} \\{= {{t\;{r\left\lbrack {{C_{l\; k}^{R}\left\lbrack m^{\prime} \right\rbrack} \cdot X_{l\; k}^{R}} \right\rbrack}} - {t\;{r\left\lbrack {{C_{l\; k}^{l}\left\lbrack m^{\prime} \right\rbrack} \cdot X_{l\; k}^{l}} \right\rbrack}}}} \\{X_{l\; k} \equiv {a_{k} \cdot a_{l}^{H}} \equiv {X_{l\; k}^{R} + {j\; X_{l\; k}^{l}}}} \\{{C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \equiv {{C_{l\; k}^{R}\left\lbrack m^{\prime} \right\rbrack} + {j\;{C_{l\; k}^{l}\left\lbrack m^{\prime} \right\rbrack}}}}\end{matrix} & (8)\end{matrix}$

The use of the X-matrix as illustrated above advantageously allowsreusing the X-matrix multiplies for all virtual users associated with aphysical user and for all m′ (i.e., m=0, 1). The remaining calculationscan be expressed as a single real dot product of length 2L2=32. Thecalculations can be performed, for example, in 16-bit fixed point math.Then, the total operations can amount to 1.5(4)(K_(v)L)2=3.84 MOPSresulting in a processing requirement of 2.90 GOPS. The X-matrixmultiplies, when amortized, amount to an additional 0.7 GOPS. Thus, thetotal processing requirement can be 3.60 GOPS.

The matched-filter outputs can be obtained from the above Equation (5)as follows:

$\begin{matrix}{{y_{l}\lbrack m\rbrack} = {{{r_{l\; l}\lbrack 0\rbrack}{b_{l}\lbrack m\rbrack}} + {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\left\lbrack {- 1} \right\rbrack}{b_{k}\left\lbrack {m + 1} \right\rbrack}}} + {\sum\limits_{k = 1}^{K_{v}}{\left\lbrack {{r_{l\; k}\lbrack 0\rbrack} - {{r_{l\; l}\lbrack 0\rbrack}\delta_{l\; k}}} \right\rbrack{b_{k}\lbrack m\rbrack}}} + {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\lbrack 1\rbrack}{b_{k}\left\lbrack {m - 1} \right\rbrack}}} + {\eta_{l}\lbrack m\rbrack}}} & (9)\end{matrix}$

wherein the first term represents a signal of interest, and theremaining terms represent Multiple Access Interference (MAI) and noise.The illustrated embodiment uses a Multistate Decision Feedbackinterference Cancellation (MDFIC) algorithm can be utilized to solve forthe symbol estimates in accord with the following relationship:

$\begin{matrix}{{{\hat{b}}_{l}\lbrack m\rbrack} = {s\; i\; g\; n\left\{ {{y_{l}\lbrack m\rbrack} - {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\left\lbrack {- 1} \right\rbrack}{{\hat{b}}_{k}\left\lbrack {m + 1} \right\rbrack}}} - {\sum\limits_{k = 1}^{K_{v}}{\left\lbrack {{r_{l\; k}\lbrack 0\rbrack} - {{r_{l\; l}\lbrack 0\rbrack}\delta_{l\; k}}} \right\rbrack{{\hat{b}}_{k}\lbrack m\rbrack}}} + {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\lbrack 1\rbrack}{{\hat{b}}_{k}\left\lbrack {m - 1} \right\rbrack}}}} \right\}}} & (10)\end{matrix}$

with initial estimates given by hard decisions on the matched-filterdetection statistics,{circumflex over (b)} _(l) [m]=sign{y _(l) [m]}.

A further appreciation of these and alternate MDFIC techniques may beattained by reference to An MDFIC technique which is described in anarticle by T. R. Giallorenzi and S. G. Wilson, titled, “Decisionfeedback multi-user receivers for asynchronous CDMA systems”, publishedin IEEE Global Telecommunications Conference, pages 1677–1682 (June1993), and herein incorporated by reference. Related techniques, knownas , is closely related to Successive Interference Cancellation (SIC)and Parallel Interference Cancellation (PIC), can be used in addition orinstead.

In the illustrated embodiment, the new estimates {circumflex over(b)}_(l)[m] are immediately introduced back into the interferencecancellation as they are calculated. Hence at any given cancellationstep, the best available symbol estimates are used. In one embodiment,the above iteration can be performed on a block of 20 symbols, whichrepresents two WCDMA time slots. The R-matrices are assumed to beconstant over this period. The sign detector in Equation (10) above canbe replaced by a hyperbolic tangent detector to improve performanceunder high input BER. A hyperbolic tangent detector has a single slopeparameter which varies from one iteration to another.

The three R-matrices (R[−1], R[0] and R[1]) are each K_(v)×K_(v) insize. Hence, the total number of operation per iteration is 6K_(v) ².The computational complexity of the MDFIC algorithm depends on the totalnumber of virtual users, which in turn depends on the mix of users atvarious spreading factors. For K_(v)=200 users (e.g. 100 low-rateusers), the computation requires 240,000 operations. In one embodiment,two iterations are employed which require a total of 480,000 operations.For real-time applications, these operations must be performed in 1/15ms or less. Thus, the total processing requirement is 7.2 GOPS.Computational complexity is markedly reduced if a threshold parameter isset such that IC is performed only for those |y_(l)[m]| below thethreshold. If |y_(l)[m]| is large, there is little doubt as to the signof b_(l)[m], and IC need not be performed. The value of the thresholdparameter can be variable from stage to stage.

C-Matrix Calculation

As discussed above, the C-matrix elements are utilized to calculate theR-matrices, which in turn are employed by an MDF InterferenceCancellation routine. The C-matrix elements can be calculated byutilizing different techniques, as described elsewhere herein. In oneapproach, the C-matrix elements are calculated directly whereas inanother approach the C-matrix elements are computed from the Γ-matrixelements, as discussed in detail below and illustrated elsewhere herein.

More particularly, in one method for calculating the C matrix elements,each C-matrix element can be calculated as a dot product between the kthuser's waveform and the lth user's code stream, each offset by somemultipath delay. For this method of calculation, each time a user'smultipath profile changes, all the C-matrix elements associated with thechanged profile need to be recalculated. A user's profile can changevery rapidly, for example, every 100 msec or faster, therebynecessitating frequent updates of the C-matrix elements. Such frequentupdates of the C-matrix elements can give rise to a large amount ofoverhead associated with computations that need to be performed beforeobtaining each dot product. In fact, obtaining the C-matrix elements bythe above approach may require dedicating an entire processor forperforming the requisite calculations.

Another approach according to the teachings of the invention forcalculating the C-matrix elements pre-calculates the code correlationsup-front when a user is added to the system. The calculations areperformed over all possible code offsets and can be stored, for example,in a large array (e.g., approximately 21 Mbytes in size), hereinreferred to as the Γ-matrix. This allows updating C-matrix elements whena user's profile changes by extracting the appropriate elements from theGamma matrix and performing minor calculations. Since the Γ-matrixelements are calculated for all code offsets, FFT can be effectivelyemployed to speed up the calculations. Further, because all code offsetsare pre-calculated, rapidly changing multipath profiles can be readilyaccommodated. This approach has a further advantage in that it minimizesthe use of resources that need to be allocated for extracting theC-matrix elements when the number of users accessing system is constant.

C-Matrix Elements Expressed in Terms of Code Correlations

As discussed above, the R-matrix elements can be given in terms of theC-matrix elements as follows:

$\begin{matrix}{{{{{\hat{\rho}}_{l\; k}\left\lbrack m^{\prime} \right\rbrack}A_{l}A_{k}} = {\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {{\hat{a}}_{l\; q}^{*}{a_{k\; q^{\prime}} \cdot {C_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack}}} \right\}}}}}{{C_{l\; k\; q\; q^{\prime}}\left\lbrack m^{\prime} \right\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{s_{k}\left\lbrack {{n\; N_{c}} + {m^{\prime}T} + {\hat{\tau}}_{l\; q} - {\hat{\tau}}_{k\; q^{\prime}}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}}} & (11)\end{matrix}$

where C_(lkqq′)[m′] is a five-dimensional matrix of code correlations.Both l and k range from 1 to K_(v), where K_(v) is the number of virtualusers. The indices q and q′ range from 1 to L, representing the numberof multipath components, which in this exemplary embodiment is assumedto be 4. The symbol period offset m′ ranges from −1 to 1. The totalnumber of matrix elements to be calculated is thenN_(C)=3(K_(v)L)²=3(800)²=1.92M complex elements, requiring 3.84 MB ofstorage if each element is a byte. The following symmetry property ofthe C-matrix elements can be utilized to halve the storage requirement,for example, in this case to 1.92 MB:

$\begin{matrix}{{C_{k\; l\; q^{\prime}q}\left\lbrack {- m^{\prime}} \right\rbrack} = {\frac{N_{l}}{N_{k}}{C_{l\; k\; q\; q^{\prime}}^{*}\left\lbrack m^{\prime} \right\rbrack}}} & (12)\end{matrix}$

It is evident from the above Equation (12) that each element ofC_(lkqq′)[m′] is formed as a complex dot product between a code vectorc_(l) and a waveform vector S_(kqq′). In this exemplary embodiment, thelength of the code vector is 256. The waveform S_(k)[t] , hereinreferred to as the signature waveform for the kth virtual user, isgenerated by applying a pulse-shaping filter g[t] to the spread codesequence c_(k)[n] as follows:

$\begin{matrix}{{s_{k}\lbrack t\rbrack} = {\sum\limits_{p = 0}^{N - 1}{{g\left\lbrack {t - {p\; N_{c}}} \right\rbrack}{c_{k}\lbrack p\rbrack}}}} & (13)\end{matrix}$

where N=256 and g[t] is the raised-cosine pulse shape. Since g[t] is araised-cosine pulse as opposed to a root-raised-cosine pulse, thesignature waveform s_(k)[t] includes the effects of filtering by thematched chip filter. For spreading factors less than 256, some of thechips c_(k)[p] are zero. The length of the waveform vector s_(k)[t] isL_(g)+255N_(c), where L_(g) is the length of the raised-cosine pulsevector g[t] and N_(c) is the number of samples per chip. The values forthese parameters in this exemplary embodiment are selected to beL_(g)=48 and N_(c)−4. The length of the waveform vector is then 1068,but for performing the dot product, it is accessed at a stride ofN_(c)=4, which results in an effective length of 267.

In this exemplary embodiment, the raised-cosine pulse vector g[t] isdefined to be non-zero from t=−L_(g)/2+1:L_(g)/2, with g[0]=1. With thisdefinition the waveform s_(k)[t] is non-zero in a range fromt=−L_(g)/2+1: L_(g)/2+255N_(c).

By combining Equations (11) and (13), the calculation of the C-matrixelements can be expressed directly in terms of the user codecorrelations. These correlations can be calculated up front and stored,for example, in SDRAM. The C-matrix elements expressed in tees of thecode correlations Γ_(lk)[m] are:

$\begin{matrix}{{{\begin{matrix}{{C_{{lkqq}^{\prime}}\left\lbrack m^{\prime} \right\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{s_{k}\left\lbrack {{nN}_{c} + {m^{\prime}T} + {\hat{\tau}}_{lq} - {\hat{\tau}}_{{kq}^{\prime}}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{p}{{g\left\lbrack {{\left( {n - p} \right)N_{c}} + {m^{\prime}T} + {\hat{\tau}}_{lq} - {\hat{\tau}}_{{kq}^{\prime}}} \right\rbrack} \cdot {c_{k}\lbrack p\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{m}{{g\left\lbrack {{mN}_{c} + \tau} \right\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}}} \\{= {\sum\limits_{m}{{{g\left\lbrack {{mN}_{c} + \tau} \right\rbrack} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}}} \\{= {\sum\limits_{m}{{g\left\lbrack {{mN}_{c} + \tau} \right\rbrack} \cdot {\Gamma_{lk}\lbrack m\rbrack}}}}\end{matrix}{\Gamma_{lk}\lbrack m\rbrack}} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}}\mspace{200mu}{\tau \equiv {{m^{\prime}T} + {\hat{\tau}}_{lq} - {\hat{\tau}}_{{kq}^{\prime}}}}} & (14)\end{matrix}$

Since the pulse shape vector g[n] is of length L_(g), at most2L_(g)/N_(c)=24 real macs need to be performed to calculate each elementC_(lkqq)[m′] (the factor of 2 arises because the code correlationsΓ_(lk)[m] are complex). For a given τ, the method of the inventionefficiently calculates the range of m values for which g[mN_(c)+τT] isnon-zero as described below. The minimum value of m is given bym_(min1)N_(c)+τ=−L_(g)/2+1, and τ is given by τ=m′NN_(c)+τ_(lq)−τ_(kq′).If each τ value is decomposed as τ_(lq)=n_(lq)N_(c)+p_(lq), thenm_(min1)=ceil[(−τ−L_(g)/2+1)/N_(c)]=−m′N−n_(lq)+n_(kq′)−L_(g)/(2N_(c))+ceil[(p_(kq′)−P_(lq)+1)/N_(c)],where ceil[(p_(kq′)−p_(lq)+1)/N_(c)] will be either 0 or 1. It isconvenient to set this value to 0. In order to avoid accessing valuesoutside the allocation for g[n], g[n]=0.0 forn=−L_(g)/2:−L_(g)/2−(N_(c)−1). All but one of the N_(c) ² possiblevalues for ceil[(p_(kq′)−P_(lq)+1)/N_(c)] are 0.

Accordingly, the following relation holds:m _(min1) =−m′N−n _(lq) +n _(kq′) −L _(g)/(2N_(c))  (15)

wherein L_(g) is divisible by 2N_(c), and L_(g)/(2N_(c)) is a systemconstant.

Since, the maximum value of m is given by m_(max1)N_(c)+τ=L_(g)/2, thefollowing holds:m _(max1)=floor[(−τ+L _(g)/2)/N _(c) ]=−m′N−n _(lq) +n _(kq′) +L_(g)/(2N _(c))+floor[(p _(kq′−) p _(lq))/N _(c)].

Further, floor[(P_(kq′)−P_(lq)/N) _(c)] can be either −1or 0. In thisexemplary embodiment, it is convenient to set this value to 0. In orderto avoid accessing values outside the allocation for g[n], g[n] is setto 0.0 (g[n]=0.0) for n=−L_(g)/2+1: L_(g)/2^(2+N) _(c). It is noted thathalf of the N_(c) ²possible values for floor[(p_(kq′)−p_(lp))/N_(c)]are0. Accordingly, the following relation holds:m _(max1) =−m′N−n _(lq)+n_(kq′) +L _(g)/(2N _(c))  (16)

The values of m_(min1) and m_(max1) are quickly calculable.

The calculation of the C-matrix elements typically requires a smallsubset of the Γ matrix elements. The Γ matrix elements can be calculatedfor all values of m by utilizing Fast Fourier Transform (FFT) asdescribed in detail below.

Using FFT to Calculate the Γ-matrix Elements

It was shown above that the Γ-matrix elements can be represented as aconvolution. Accordingly, the FFT convolution theorem can be exploitedto calculate the Γ-matrix elements. From the above Equation (14), theΓ-matrix elements are defined as follows:

$\begin{matrix}{{\Gamma_{lk}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N - 1}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}} & (17)\end{matrix}$

where N=256. Three streams are related by this equation. In order toapply the convolution theorem, these three streams are defined over thesame time interval. The code streams c_(k)[n] and c_(l)[n] are non-zerofrom n=0:255. These intervals are based on the maximum spreading factor.For higher data-rate users, the intervals over which the streams arenon-zero are reduced further. The intervals derived from the highestspreading factor are of particular interest in defining a commoninterval for all streams because they represent the largest intervals.The common interval allows the FFTs to be reused for all userinteractions.

With reference to FIG. 15, the range of values of m for which Γ_(lk)[m]is non-zero can be derived from the above intervals. The maximum valueof m is limited by n−m≧0, which gives255−m _(max)=0→m _(max)=255  (18)

and the minimum value of m is limited by n−m≦255, which gives0−m _(min)=255→m _(min)=−255  (19)

To achieve a common interval for all three streams, an interval definedby m=−M/2: M/2−1, M=512 is selected. The streams are zero-padded to fillup the interval, if needed.

Accordingly, the DFT and IDFT of the streams are given by the followingrelations:

$\begin{matrix}{{{C_{l}\lbrack r\rbrack} = {\sum\limits_{n = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{c_{l}\lbrack n\rbrack} \cdot {\mathbb{e}}^{{- {j2\pi}}\;{{nr}/M}}}}}{{c_{l}\lbrack n\rbrack} = {\frac{1}{M}{\sum\limits_{r = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{C_{l}\lbrack r\rbrack} \cdot {\mathbb{e}}^{{j2\pi}\;{{nr}/M}}}}}}{{which}\mspace{14mu}{gives}}} & (20) \\\begin{matrix}{{\Gamma_{lk}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{c_{k}\left\lbrack {n - m} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \\{= \begin{matrix}{\frac{1}{2N_{l}M^{2}}{\sum\limits_{n = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{\sum\limits_{r = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{C_{k}\lbrack r\rbrack} \cdot {\mathbb{e}}^{{j2\pi}\;{({n - m})}{r/M}}}}}} \\{{\sum\limits_{r^{\prime} = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{C_{l}^{*}\left\lbrack r^{\prime} \right\rbrack} \cdot {\mathbb{e}}^{{- {j2\pi}}\;{{nr}^{\prime}/M}}}}\mspace{135mu}}\end{matrix}} \\{= {\frac{1}{2N_{l}M^{2}}{\sum\limits_{r = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{{C_{k}\lbrack r\rbrack} \cdot {\mathbb{e}}^{{- {j2\pi}}\;{{mr}/M}}}{\sum\limits_{r^{\prime} = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{C_{l}^{*}\left\lbrack r^{\prime} \right\rbrack}{\sum\limits_{n = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{\mathbb{e}}^{{j2\pi}\;{{n{({r - r^{\prime}})}}/M}}}}}}}}} \\{= {\frac{1}{2N_{l}M}{\sum\limits_{r = {- \frac{M}{2}}}^{\frac{M}{2} - 1}{{{C_{k}\lbrack r\rbrack} \cdot {C_{l}^{*}\lbrack r\rbrack}}{\mathbb{e}}^{{- {j2\pi}}\;{{mr}/M}}}}}}\end{matrix} & (21)\end{matrix}$

Hence, Γ_(lk)[m] can be calculated for all values of m by utilizing FFT.Based on the analysis presented above, many of these values will be zerofor high data rate users. In this exemplary embodiment, only thenon-zero values are stored in order to conserve storage space. Thevalues of m for which Γ_(lk)[m] is non-zero can be determinedanalytically, as described in more detail below and illustratedelsewhere herein.

Storage and Retrieval of Γ-matrix Elements

As discussed above, the values of the Γ-matrix elements which arenon-zero need to be determined for efficient storage of the Γ-matrix.For high data rate users, certain elements c_(l)[n] are zero, evenwithin the interval n=0:N−1, N=256. These zero values reduce theinterval over which Γ_(lk)[m] is non-zero. In order to determine theinterval for non-zero values consider the following relations:

$\begin{matrix}{{\Gamma_{lk}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N - 1}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}} & (22)\end{matrix}$

The index j_(l) for the lth virtual user is defined such that c_(l)[n]is non-zero only over the interval n=j_(l)N_(l): j_(l)N_(l)+N_(l)−1.Correspondingly, the vector c_(k)[n] is non-zero only over the intervaln=j_(k)N_(k): j_(k)N_(k)+N_(k)−1. Given these definitions, Γ_(lk)[m] canbe rewritten as

$\begin{matrix}{{\Gamma_{lk}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N_{l} - 1}{{c_{l}^{*}\left\lbrack {n + {j_{l}N_{l}}} \right\rbrack} \cdot {c_{k}\left\lbrack {n + {j_{l}N_{l}} - m} \right\rbrack}}}}} & (23)\end{matrix}$

The minimum value of m for which Γ_(lk)[m] is non-zero ism _(min2) =−j _(k) N _(k) +j _(l) N _(l) −N _(k)+1  (24)

and the maximum value of m for which Γ_(lk)[m] is non-zero ism _(max 2) =N _(l)1−j _(k) N _(k) +j _(l) N _(l)  (25)

The total number of non-zero elements is then

$\begin{matrix}\begin{matrix}{m_{total} \equiv {m_{\max\; 2} - m_{\min\; 2} + 1}} \\{= {N_{l} + N_{k} - 1}}\end{matrix} & (26)\end{matrix}$

The table below provides the number of bytes per l,k virtual-user pairbased on 2 bytes per element—one byte for the real part and one byte forthe imaginary part.

N_(k) = 256 128 64 32 16 8 4 N_(l) = 256 1022 766 638 574 542 526 518128 766 510 382 318 286 270 262  64 638 382 254 190 158 142 134  32 574318 190 126 94 78 70  16 542 286 158 94 62 46 38  8 526 270 142 78 46 3022  4 518 262 134 70 38 22 14

The memory requirements for storing the Γ matrix for a given number ofusers at each spreading factor can be determined as described below. Forexample, for K_(q) virtual users at spreading factor N_(q)≡2^(8−q),q=0:6, where K_(q) is the qth element of the vector K (some elements ofK may be zero), the storage requirement can be computed as follows. LetTable 1 above be stored in matrix M with elements M_(qq′). For example,M₀₀=1022, and M₀₁=766. The total memory required by the Γ matrix inbytes is then given by the following relation

$\begin{matrix}\begin{matrix}{M_{bytes} = {\sum\limits_{q = 0}^{6}\left\{ {{\frac{K_{q}\left( {K_{q} + 1} \right)}{2}M_{qq}} + {\sum\limits_{q^{\prime} = {q + 1}}^{6}{K_{q}K_{q^{\prime}}M_{{qq}^{\prime}}}}} \right\}}} \\{= {\frac{1}{2}{\sum\limits_{q = 0}^{6}\left\{ {{K_{q}M_{qq}} + {\sum\limits_{q^{\prime} = 0}^{6}{K_{q}K_{q^{\prime}}M_{{qq}^{\prime}}}}} \right\}}}}\end{matrix} & (27)\end{matrix}$

For example, for 200 virtual users at spreading factor N₀=256,K_(q)=200δ_(q0), which in turn results inM_(bytes)½K₀(K₀+1)M₀₀=100(201)(1022)=20.5 MB. For 10 384 Kbps users,K_(q)=K₀δ_(q0)+K₆δ_(q6) with K₀=10 and K₆₌640, which results in astorage requirement that is given by the following relations:M _(bytes)=½K ₀(K ₀+1)M ₀₀ +K ₀ K ₆ M ₀₆+½K ₆(K ₆+1)M₆₆=5(11)(1022)+10(640)(518)+320(641)(14)=6.2MB.

The Γ-matrix data can be addressed, stored, and accessed as describedbelow. In particular, for each pair (l,k), k>=l, there are 1 complexΓ_(lk)[m] values for each value of m, where m ranges from m_(min2) tom_(max 2), and the total number of non-zero elements ism_(total)=m_(max 2)−m_(min2)+1. Hence, for each pair (l,k), k>=l, thereexists 2m_(total) time-contiguous bytes.

In one embodiment, an array structure is created to access the data, asshown below:

struct { int m_min2; int m_max2; int m_total; char * Glk; }G_info[N_VU_MAX][N_VU_MAX];

The C-matrix data can then be retrieved by utilizing the followingexemplary algorithm:

m_(min2) = G_info[l][k].m_min2 m_(max2) = G_info[l][k].m_max2 N_(g) =L_(g)/N_(c) N1 = m'*N − L_(g)/(2N_(c)) for m' = 0:1 for q = 0:L −1 forq' = 0:L −1 τ = m'T + τ_(lq) − τ_(kq') m_(min1) = N1 − n_(lq) + n_(kq')m_(max1) = m_(minl) + N_(g) m_(min) = max[m_(min1) , m_(min2)] m_(max) =min[m_(max1) , m_(max2)] if m_(max) >= m_(min) m_(span) = m_(max) −m_(min) + 1 sum1 = 0.0; ptr1 = &G_info[l][k].Glk[m_(min)] ptr2 =&g[m_(min) * N_(c) + τ] while m_(span) > 0 sum1 += (*ptr1++) * (*ptr2++)m_(span)−− end C[m'][l][k][q][q'] = sum1 end end end end

Another method for calculating the Γ-matrix elements, herein referred toas the direct method, performs a direct convolution, for example, byemploying the SALzconvx function, to compute these elements. This directmethod is preferable when the vector lengths are small. As anillustration of the time required for performing calculations, The tablebelow provides exemplary timing data based on a 400 MHz PPC7400 with 16MHz, 2 MB L2 cache, wherein the data is assumed to be resident in L1cache. The performance loss for L2 cache resident data is not severe.

M_(total) N_(l) Timing (μs) GFLOPS 1024 4 19.33 1.70 1024 8 29.73 2.201024 16 50.55 2.59 1024 32 92.32 2.84 1024 64 176.53 2.97 1024 128346.80 3.47

As discussed above, FFT can also be utilized for calculating theΓ-matrix elements. The time required to perform a 512 complex FFT, within-place calculation, on a 400 MHz PPC7400 with 16 MHz, 2 MB L2 cache is10.94 As for L1 resident data. Prior to performing the final FFT, acomplex vector multiplication of length 512 needs to be performed.Exemplary timings for this computation are provided in the followingtable:

Length Location Timing (μs) GFLOPS 1024 L1 4.46 1.38 1024 L2 24.27 0.2531024 DRAM 61.49 0.100

Further, exemplary timing data for moving data between memory and theprocessor is provided in the following table:

Length Location Timing (μs) 1024 L1 1.20 1024 L2 15.34 1024 DRAM 30.05

FIG. 16 illustrates the Γ-matrix elements that need to be calculatedwhen a new physical user is added to the system. Addition of a newphysical user to the system results in adding 1+J virtual users to thesystems: that is, 1 control channel+J−256/SF data channels. The numberK_(v) represents the number of initial virtual users. Hence there are(K_(v)+1) elements added to the Γ-matrix as a result of increase in thenumber of the control channels, and J(K_(v)+1)+J(J+1)/2 elements addedas a result of increase in the number of the data channels. The totalnumber of elements added is then (J+1)[K_(v)+1+J/2]. If FFT is utilizedto perform the calculations, the total number of FFTs to be performed is(J+1)+(J+1)[K_(v)+1+J/2]. The first term represents the FFTs totransform c_(k)[n], and the second term represents the(J+1)[K_(v)+1+J/2] inverse FFTs of FFT{c_(k)[n]}*FFT{c_(l)*[n]}. Thetime to perform the complex 512 FFTs can be, for example, 10.94 μs,whereas the time to perform the complex vector multiply and the complex512 FFT can be, for example, 24.27/2+10.94=23.08 μs.

In order to provide illustrative examples of processing times, two casesof interest are considered below. In the first case scenario, a voiceuser is added to the system while K=100 users (K_(v)=200 virtual users)are accessing the system. Not all of these users are active. The controlchannels are always active, but the data channels have activity factorAF=0.4. The mean number of active virtual users is then K+AF*K=140. Thestandard deviation is σ=√{square root over (K·AF·(1−AF))}=4.90.Accordingly, there are K_(v)<140+3σ<155 active user with a highprobability.

The second case, which represents a more demanding scenario, arises whena single 384 Kbps data user is added while a number of users areaccessing the system. A single 384 Kbps data user adds interferenceequal to (0.25+0.125*100)/(0.25+0.400*1)˜=20 voice users. Hence, thenumber of voice users accessing the system must be reduced toapproximately K=100−20=80 (K_(v)=160). The 3σ number of active virtualusers is then 80+(0.125)80+3(3.0)=99 active virtual users. The reasonthis scenario is more demanding is that when a single 384 Kbps data useris added to the system, J+1=64+1=65 virtual users are added to thesystem.

In the first case scenario in which there are K_(v)=200 virtual usersaccessing the system and a voice user is added to the system (J=1), thetotal time to add the voice user can be (1+1)(10.94μs)+(1+1)[200+1+½](23.08 μs)=9.3 ms.

For the second scenario in which there are K_(v)=160 virtual usersaccessing the system and a 384 Kbps data user is added (J=64), the totaltime to add the 384 Kbps user can be (64 +1)(10.94μs)+(64+1)[160+1+64/2](23.08 μs)=290 ms, which is significantly largerthan 9.3 ms. Hence, at least for high data-rate user, the Γ-matrixelements are calculated via convolutions.

In the direct method of calculating the Γ-matrix elements, the SALzconvx function is utilized to perform the following convolution:

$\begin{matrix}{{\Gamma_{lk}\lbrack m\rbrack}\begin{matrix}{\equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N_{l} - 1}{{c_{l}^{*}\left\lbrack {n + {j_{l}N_{l}}} \right\rbrack} \cdot {c_{k}\left\lbrack {n + {j_{l}N_{l}} - m} \right\rbrack}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N_{k} - 1}{{c_{l}^{*}\left\lbrack {n + {j_{k}N_{k}} + m} \right\rbrack} \cdot {c_{k}\left\lbrack {n + {j_{k}N_{k}}} \right\rbrack}}}}}\end{matrix}} & (28)\end{matrix}$

For each value of m, N_(min)=min{N_(p)N_(k)} complex macs (cmacs) needto be performed. Each cmac requires 8 flops, and there arem_(total)=N_(l)+N_(k)−1 m-values to calculate. Hence, the total numberof flops is 8N_(min)(N_(l)+N_(k)−1). In the following, it is assumedthat the convolution calculation is performed at 1.50 GOPs=1500 ops/μs.The time required to perform the convolutions is presented in the tablebelow

N_(k) = 256 128 64 32 16 8 4 N_(l) = 256 697.69 261.46 108.89 48.8923.13 11.22 5.53 128 261.46 174.08 65.19 27.14 12.20 5.76 2.79  64108.89 65.19 43.35 16.21 6.74 3.03 1.43  32 48.98 27.14 16.21 10.75 4.011.66 0.75  16 23.13 12.20 6.74 4.01 2.65 0.98 0.41  8 11.22 5.76 3.031.66 0.98 0.64 0.23  4 5.53 2.79 1.43 0.75 0.41 0.23 0.15

The total time to calculate the Γ-matrix is then given by the followingrelation:

$\begin{matrix}\begin{matrix}{{T_{\Gamma}(K)} = {\sum\limits_{q = 0}^{6}\left\{ {{\frac{K_{q}\left( {K_{q} + 1} \right)}{2}T_{qq}} + {\sum\limits_{q^{\prime} = {q + 1}}^{6}{K_{q}K_{q^{\prime}}T_{{qq}^{\prime}}}}} \right\}}} \\{= {\frac{1}{2}{\sum\limits_{q = 0}^{6}\left\{ {{K_{q}T_{qq}} + {\sum\limits_{q^{\prime} = 0}^{6}{K_{q}K_{q^{\prime}}T_{{qq}^{\prime}}}}} \right\}}}} \\{= {\frac{1}{2}\left\lbrack {{K \cdot {{diag}(T)}} + {K^{T} \cdot T \cdot K}} \right\rbrack}}\end{matrix} & (29)\end{matrix}$

where T_(qq) are the elements in the above Table 5. Now suppose K′=K+Δ,where Δ_(q)=J_(x)δ_(qx)+J_(y)δ_(qy), and where x and y are not equal.Then

$\begin{matrix}\begin{matrix}{{T_{\Gamma}(K)} \equiv {{T_{\Gamma}\left( K^{\prime} \right)} - {T_{\Gamma}(K)}}} \\{{= {{\frac{1}{2}{J_{x}\left( {J_{x} + 1} \right)}T_{xx}} + {\frac{1}{2}{J_{y}\left( {J_{y} + 1} \right)}T_{yy}} + \;{J_{x}J_{y}T_{xy}} + {\sum\limits_{q = 0}^{6}\;{K_{q}\left\{ {{J_{x}T_{xq}} + {J_{y}T_{yq}}} \right\}}}}}\;}\end{matrix} & (30)\end{matrix}$

In the first scenario, there are K_(v)=200 virtual users accessing thesystem and a voice user is added to the system (J=1). Hence,K_(q)=K_(v)δ_(q0) (SF=256), K_(v)=200, J_(x)=J=2 and J_(y)=0. The totaltime is then½J(J+1)T ₀₀ +JK _(v) T ₀₀=(0.5)(2)(3)(0.70 ms)+(2)(200)(0.70 ms)=283 ms

This number is large enough to require that for voice users, at least,the Γ-matrix elementst be calculated via FFTs.

For the second scenario, there are K_(v)=160 virtual users accessing thesystem and a 384 Kbps data user is added to the system (J=64). Hence,K_(q)=K_(v)δ_(q0)(SF=256), K_(v)=160,J_(x)=1 (control) and J_(y)=J=64(data). The total time is then

(K_(v) + 1)T₀₀ + J(K_(v) + 1)T₀₆ + (J + 1)(J/2)T₆₆ = (161)(697.7  μ s) + (64)(161)(5.53  μ s) + (65)(32)(0.15  μ s) = 112.33  ms + 56.98  ms + 0.31  ms = 169.62  ms

Accordingly, these calculations should also be performed by utilizingFFT, which can require, for example, 23.08 μs per convolution. Inaddition, 1 FFT is required to compute FFT{c_(k)*[n]}) for the singlecontrol channel. This can require an additional 10.94 μs. The totaltime, then, to add the 384 Kbps user is10.94 μs+(161)(23.08)μs+(64)(161)(5.53)μs+(65)(32)(0.15)μs==61.02 mst

Γ-matrix Elements to SDRAM

With reference to above Equation (27), the size of the Γ-matrix in bytesis given by the following relation:

$\begin{matrix}\begin{matrix}{{M_{b}(K)} = {\sum\limits_{q = 0}^{6}\left\{ {{\frac{K_{q}\left( {K_{q} + 1} \right)}{2}M_{qq}} + {\sum\limits_{q^{\prime} = {q + 1}}^{6}{K_{q}K_{q^{\prime}}M_{{qq}^{\prime}}}}} \right\}}} \\{= {\frac{1}{2}{\sum\limits_{q = 0}^{6}\left\{ {{K_{q}M_{qq}} + {\sum\limits_{q^{\prime} = 0}^{6}{K_{q}K_{q^{\prime}}M_{{qq}^{\prime}}}}} \right\}}}} \\{= {\frac{1}{2}\left\lbrack {{K \cdot {{diag}(M)}} + {K^{T} \cdot M \cdot K}} \right\rbrack}}\end{matrix} & (31)\end{matrix}$

Now suppose K′=K+Δ, where Δ_(q)=J_(x)δ_(qx)+J_(y)δ_(qy), and where x andy are not equal. Then

$\begin{matrix}{{{\Delta\; M_{b}} \equiv {{M_{b}\left( K^{\prime} \right)} - {M_{b}(K)}}} = {{\frac{1}{2}{J_{x}\left( {J_{x} + 1} \right)}M_{xx}} + {\frac{1}{2}{J_{y}\left( {J_{y} + 1} \right)}M_{yy}} + b + {\sum\limits_{q = 0}^{6}{K_{q}\left\{ {{J_{x}M_{xq}} + {J_{y}M_{yq}}} \right\}}}}} & (32)\end{matrix}$

Consider a first exemplary scenario in which K_(q)=200δ_(q0) (SF=256)and a single voice user is added to the system: J_(x)=2 (data pluscontrol), and J_(y)=0. The total number of bytes to be written to SDRAMis then 0.5(2)(3)(1022)+200(2)(1022)=0.412 MB. Assuming a SDRAM writespeed of 133 MHz*8 bytes*0.5=532 MB/s, the time required to writeΓ-matrix to SDRAM is then 0.774 ms.

For additional illustration of the time required for storing theΓ-matrix, consider a second scenario in which K_(q=)1600δ_(q0) (SF=256),and a single 384 Kbps (SF=4) user is added to the system: J_(x)=1(control) and J_(y)=64 (data). The total number of bytes is then0.5(1)(2)(1022)+0.5(64)(65)(14)+160{1(1022)+64(518)}=5.498 MB. The SDRAMwrite speed is 133 MHz*8 bytes*0.5=532 MB/s. The time to write to SDRAMis then 10.33 ms.

Packing the Gamma-Matrix Elements in SDRAM

In this exemplary embodiment, the maximum total size of the Γ-matrix is20.5 MB. If it is assumed that in order to pack the matrix, everyelement must be moved (this is the most demanding scenario), then for aSDRAM speed of 133 MHz*8 bytes*0.5=532 MB/s, the move time is then2(20.5 MB)/(532 MB/s)=77.1 ms. If the Γ-matrix is divided over threeprocessors, this time is reduced by a factor of 3. The packing can bedone incrementally, so there is no strict time limit.

Extracting Gamma-Matrix Elements from SDRAM

As described above, in this exemplary embodiment, the C-matrix data isretrieved by utilizing the following algorithm:

m_(min2) = G_info[l][k].m_min2 m_(max2) = G_info[l][k].m_max2 N_(g) =L_(g)/N_(c) N1 = m'*N − L_(g)/(2N_(c)) for m' = 0:1 for q = 0:L −1 forq' = 0:L −1 τ = m'T + τ_(lq) − τ_(kq') m_(min1) = N1 − n_(lq) + n_(kq')m_(max1) = m_(minl) + N_(g) m_(min) = max[m_(min1) , m_(min2)] m_(max) =min[m_(max1) , m_(max2)] if m_(max) >= m_(min) m_(span) = m_(max) −m_(min) + 1 sum1 = 0.0; ptr1 = &G_info[l][k].Glk[m_(min)] ptr2 =&g[m_(min) * N_(c) + τ] while m_(span) > 0 sum1 += (*ptr1++) * (*ptr2++)m_(span)−− end C[m'][l][k][q][q'] = sum1 end end end end

The time requirements for calculating the Γ-matrix elements in thisexemplary embodiment, when a new user is added to the system wasdiscussed above. The time requirements for extracting the correspondingC-matrix elements are discussed below.

The Γ_(lk)[m] elements are accessed from SDRAM. It is highly likely thatthese values will not be contained in either L1 or L2 cache. For a given(l,k) pair, however, the spread in τ is likely to be, for most cases,less than 8 μs (i.e. for a 4 μs delay spread), which equates to (8 μs)(4chips/μs)(2 bytes/chip)=64 bytes, or 2 cache lines. In an embodiment inwhich data is read in for two values of m′, a total of 4 cache linesmust be read. This will require 16 clocks, or about 16/133=0.12 μs.However, in some embodiments, accesses to SDRAM may be performed atabout 50% efficiency so that the required time is about 0.24 μs.

If a user l=x is added to the system, the elements C[m′][x][k][q][q′]for all m′, k, q and q′ need to be fetched. As indicated above, all them′, q and q′ values are typically contained in 4 cache lines. Hence, ifthere are K_(v) virtual users, 4K_(v) cache lines need to be read,thereby requiring 32K_(v) clocks, where the number of clocks has beendoubled to account for the 50% efficiency in accessing the SDRAM. Ingeneral, addition off J+1 virtual users to the system at a time,requires 32K_(v)(J+1) clocks.

In one example where there are 155 active virtual users and a new voiceuser is added to the system, the time required to read in the C-matrixelements can be 32(155)(1+1) clocks/(133 clocks/μs)=74.6 μs. The presentindustry standard hold time t_(h) for a voice call is 140 s. The averagerate λ of users added to the system can be determined from λt_(h)=K,where K is the average number of users utilizing the system. For K=100users, λ=100/140 s=1 user are added per 1.4 s.

In another example where there are 99 active virtual users and a 384Kbps user is added to the system, the time required to read in theC-matrix elements can be 32(99)(64+1) clocks/(133 clocks/μs)=1.55 ms.However data users presumably will be added to the system moreinfrequently than voice users.

Time to Extract Elements When τ_(xy) Changes

Now suppose, for example, that user l=x lag q=y changes. Thisnecessitates fetching the elements C[m′][x][k][y][q′] for all m′, k andq′. All the q′ values will be contained typically in 1 cache line.Hence, 2(K_(v))(1)=2K_(v) cache lines need to be read in, therebyrequiring 16K_(v) clocks, where the number of clocks has been doubled toaccount for the 50% efficiency in accessing the SDRAM. In general, whena time lag changes, there are J+1 virtual users for which the C-matrixelements need to be updated. Such updating of the C-matrix elements canrequire 16K_(v)(J+1) clocks.

In one example in which 155 active virtual users are present and a voiceuser's profile (one lag) changes, the time required to read in theC-matrix elements can be 16(155)(1+1) clocks/(133 clocks/μs)=37.3 μs. Asdiscussed above, for high mobility users, such changes should occur at arate of about 1 per 100 ms per physical user. This equates to about onceper 1.33 ms processing interval, if there are 100 physical users. Hence,approximately 37.3 μs will be required every 1.33 ms.

In another example where there are 99 virtual users and a 384 Kbps datauser's profile (one lag) changes, the time required to read in theC-matrix elements can be 16(99)(64+1) clocks/(133 clocks/μs)=0.774 ms.However data users will have lower mobility and hence such changesshould occur infrequently.

Writing C-Matrix Elements to L2 Cache

Consider again the case where user l=x is added to the system. In such acase, the elements C[m′][x][k][q][q′] for all m′, k, q and q′ need to bewritten to cache. If there are K_(v) active virtual users, 4K_(v)L²bytes need to be written, where the number of bytes have been doubledbecause the elements are complex. In general, addition of J+1 virtualusers to the system at a time will require 4K_(v)L²(J+1) bytes to bewritten to L2 cache.

In one example, there are 155 active virtual users and a new voice useris added to the system. In this case, the time required to write theC-matrix elements can be 4(155)(16)(1+1) bytes/(2128 bytes/μs)=9.3 μs.

In another example, there are 99 active virtual users and a 384 Kbpsuser is added to the system. In such a case, the time required to writethe C-matrix elements can be 4(99)(16)(64+1) bytes/(2128 bytes/μs)=193.5μs. Data users are typically added to the system more infrequently thanvoice users.

Time to Extract Elements When τ_(xy) Changes

Consider a situation in which for user l=x lag q=y changes. In such acase, the elements C[m′][x][k][q][q′] for all m′, k and q′ need to bewritten. If there are K_(v) active virtual users, 4K_(v)L bytes need tobe written, where the number of the bytes has been doubled since theelements are complex. In general, addition of J+1 virtual users thesystem at a time will require 4K_(v)L(J+1) bytes to be written to L2cache.

In one example, there are 155 active virtual users and a voice user'sprofile (one lag) changes. In such a case, the time required to writethe C-matrix elements will be 4(155)(4)(1+1) bytes/(2128 bytes/μs)=2.33μs.

In a second case, there are 99 active virtual users and a 384 Kbps datauser's profile (one lag) changes. Then, the time required to write theC-matrix elements will be 4(99)(4)(64+1)bytes/(2128 bytes/μs)=48.4 μs.However data users will have lower mobility and hence such changestypically occur infrequently.

Packing C-Matrix Elements In L2 Cache

In this exemplary embodiment, the C-matrix elements are packed in memoryevery time a new user is added to or deleted from the system, and everytime a new user becomes active or inactive. In this embodiment, the sizeof the C-matrix is 2(3/2)(K_(v)L)²=3(K_(v)L)² bytes. If three processorsare utilized, the size per processor is (K_(v)L)² bytes. Hence, thetotal time required for moving the entire matrix within L2 cache is2(K_(v)L)² bytes/(2128 bytes/μs), where the factor of 2 accounts forread and write. By way of example, if there are 155 active virtualusers, the time required to move the C-matrix elements is 2(155*4)²bytes/(2128 bytes/μs)=0.361 ms, whereas if there are 99 active virtualusers the time required to move the C-matrix elements is 2(99*4)²bytes/(2128 bytes/μs)=0.147 ms.

Hardware Calculation of Γ-Matrix Elements

As discussed above, the C-matrix elements can be represented in terms ofthe underlying code correlations in accord with the following relation:

$\begin{matrix}{{{\begin{matrix}{{C_{{lkqq}^{\prime}}\left\lbrack m^{\prime} \right\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{s_{k}\left\lbrack {{nN}_{c} + {m^{\prime}T} + {\hat{\tau}}_{lq} - {\hat{\tau}}_{{kq}^{\prime}}} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{p}{{g\left\lbrack {{\left( {n - p} \right)N_{c}} + {m^{\prime}T} + {\hat{\tau}}_{lq} - {\hat{\tau}}_{{kq}^{\prime}}} \right\rbrack} \cdot {c_{k}\lbrack p\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\sum\limits_{m}{{g\left\lbrack {{mN}_{c} + \tau} \right\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack} \cdot {c_{l}^{*}\lbrack n\rbrack}}}}}} \\{= {\sum\limits_{m}{{{g\left\lbrack {{mN}_{c} + \tau} \right\rbrack} \cdot \frac{1}{2N_{l}}}{\sum\limits_{n}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}}} \\{= {\sum\limits_{m}{{g\left\lbrack {{mN}_{c} + \tau} \right\rbrack} \cdot {\Gamma_{lk}\lbrack m\rbrack}}}}\end{matrix}{\Gamma_{lk}\lbrack m\rbrack}} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}}\mspace{200mu}{\tau \equiv {{m^{\prime}T} + {\hat{\tau}}_{lq} - {\hat{\tau}}_{{kq}^{\prime}}}}} & (33)\end{matrix}$

The Γ-matrix represents the correlation between the complex user codes.The complex code for user l is assumed to be infinite in length, butwith only N_(l) non-zero values. The non-zero values are constrained tobe ±1±j. The Γ-matrix can be represented in terms of the real andimaginary parts of the complex user codes as follows:

$\begin{matrix}{\begin{matrix}{{\Gamma_{lk}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\left\{ {{c_{l}^{R}\lbrack n\rbrack} - {{jc}_{l}^{l}\lbrack n\rbrack}} \right\} \cdot \left\{ {{c_{k}^{R}\left\lbrack {n - m} \right\rbrack} + {{jc}_{k}^{l}\left\lbrack {n - m} \right\rbrack}} \right\}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}\left\{ {{{c_{l}^{R}\lbrack n\rbrack} \cdot {c_{k}^{R}\left\lbrack {n - m} \right\rbrack}} + {{c_{l}^{l}\lbrack n\rbrack} \cdot {c_{k}^{l}\left\lbrack {n - m} \right\rbrack}} +} \right.}}} \\{\left. {{{{jc}_{l}^{R}\lbrack n\rbrack} \cdot {c_{k}^{l}\left\lbrack {n - m} \right\rbrack}} - {{{jc}_{l}^{l}\lbrack n\rbrack} \cdot {c_{k}^{R}\left\lbrack {n - m} \right\rbrack}}} \right\}} \\{= {{\Gamma_{lk}^{RR}\lbrack m\rbrack} + {\Gamma_{lk}^{ll}\lbrack m\rbrack} + {j\left\{ {{\Gamma_{lk}^{Rl}\lbrack m\rbrack} - {\Gamma_{lk}^{lR}\lbrack m\rbrack}} \right\}}}}\end{matrix}{where}} & (34) \\{{{\Gamma_{lk}^{RR}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{R}\lbrack n\rbrack} \cdot {c_{k}^{R}\left\lbrack {n - m} \right\rbrack}}}}}{{\Gamma_{lk}^{ll}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{l}\lbrack n\rbrack} \cdot {c_{k}^{l}\left\lbrack {n - m} \right\rbrack}}}}}{{\Gamma_{lk}^{Rl}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{R}\lbrack n\rbrack} \cdot {c_{k}^{l}\left\lbrack {n - m} \right\rbrack}}}}}{{\Gamma_{lk}^{lR}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{l}\lbrack n\rbrack} \cdot {c_{k}^{R}\left\lbrack {n - m} \right\rbrack}}}}}} & (35)\end{matrix}$

Consider any one of the above real correlations, denoted

$\begin{matrix}{{\Gamma_{lk}^{XY}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{{c_{l}^{X}\lbrack n\rbrack} \cdot {c_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}}} & (36)\end{matrix}$

where X and Y can be either R or I. Since the elements of the codes arenow constrained to be ±1 or 0, the following relation can be defined:c _(l) ^(x) [n]=(1−2γ_(l) ^(x) [n])·m _(l) ^(x) [n]  (37)

where γ_(l) ^(x)[n] and m_(l) ^(x)[n] are both either zero or one. Thesequence m_(l) ^(x)[n] is a mask used to account for values of c_(l)^(x)[n] that are zero. With these definitions, the above Equation (4)becomes

$\begin{matrix}{\begin{matrix}{{\Gamma_{lk}^{XY}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n}{\left( {1 - {2{\gamma_{l}^{X}\lbrack n\rbrack}}} \right) \cdot {m_{l}^{X}\lbrack n\rbrack} \cdot \left( {1 - {2{\gamma_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}} \right) \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\left( {1 - {2{\gamma_{l}^{X}\lbrack n\rbrack}}} \right) \cdot \left( {1 - {2{\gamma_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}} \right) \cdot {m_{l}^{X}\lbrack n\rbrack} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}}} \\{= {\frac{1}{2N_{l}}{\sum\limits_{n}{\left\lbrack {1 - {2\left( {{\gamma_{l}^{X}\lbrack n\rbrack} \oplus {\gamma_{k}^{Y}\left\lbrack {n - m} \right\rbrack}} \right)}} \right\rbrack \cdot {m_{l}^{X}\lbrack n\rbrack} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}}} \\{= {\frac{1}{2N_{l}}\left\{ {{\sum\limits_{n}{{\cdot {m_{l}^{X}\lbrack n\rbrack}} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}} -} \right.}} \\{\left. {2{\sum\limits_{n}{\left( {{\gamma_{l}^{X}\lbrack n\rbrack} \oplus {\gamma_{k}^{Y}\left\lbrack {n - m} \right\rbrack}} \right) \cdot {m_{l}^{X}\lbrack n\rbrack} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}} \right\}} \\{= {\frac{1}{2N_{l}}\left\{ {{M_{lk}^{XY}\lbrack m\rbrack} - {2{N_{lk}^{XY}\lbrack m\rbrack}}} \right\}}}\end{matrix}{{M_{lk}^{XY}\lbrack m\rbrack} \equiv {\sum\limits_{n}{{\cdot {m_{l}^{X}\lbrack n\rbrack}} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}}{{N_{lk}^{XY}\lbrack m\rbrack} \equiv {\sum\limits_{n}{\left( {{\gamma_{l}^{X}\lbrack n\rbrack} \oplus {\gamma_{k}^{Y}\left\lbrack {n - m} \right\rbrack}} \right) \cdot {m_{l}^{X}\lbrack n\rbrack} \cdot {m_{k}^{Y}\left\lbrack {n - m} \right\rbrack}}}}} & (38)\end{matrix}$

where ⊕ indicates modulo-2 addition (or logical XOR).

In addition to configurations discussed elsewhere herein, FIGS. 17, 18and 19 illustrate exemplary hardware configurations for computing thefunctions M_(lk) ^(XY)[m] and N_(lk) ^(XY)[m] for calculating theΓ-matrix elements. Once the functions M_(lk) ^(XY)[m] and N_(lk)^(XY)[in] are obtained, the remaining calculations for obtaining theΓ-matrix elements can be performed in software, or hardware. In thisexemplary embodiment, these remaining calculations are performed insoftware. More particularly, FIG. 17 shows a register having an initialconfiguration subsequent to loading a code and a mask sequences.Further, FIG. 18 depicts a logic circuit for performing the requisiteboolean functions. FIG. 19 depicts the configuration of the registerafter implementing a number of shifts.

The four functions Γ_(lk) ^(XY)[m] corresponding to X, Y=R, I which arecomponents of Γ_(lk)[M] can be calculated in parallel. For K_(v)=200virtual users, and assuming that 10% of all (l, k) pairs need to becalculated in 2 ms, then for real-time operation, 0.10(200)²=4000Γ_(lk)[m] elements (all shifts) need to be computed in 2 ms, or about 2Melements (all shifts) per second. For K_(v)=128 virtual users, therequirement drops to 0.8192M elements (all shifts) per second.

In this embodiment, the Γ_(lk)[m] elements are calculated for all 512shifts. However, not all of these shifts are needed. Thus, it ispossible to reduce the number of calculations per Γ_(lk)[m] elements bycalculating only those elements that are needed.

As described in more detail elsewhere herein, in one hardwareimplementation of the invention, a single processor is utilized forperforming the C-matrix calculations whereas a plurality of processors,for example, three processors, are employed for the R-matrixcalculations, which are considerably more complex. In what follows, aload balancing method is described that calculates optimum R-matrixpartitioning points in normalized virtual user space to provide anequal, and hence balanced, computational load per processor. Moreparticularly, it is shown that a closed form recursive solution existsthat can be solved for an arbitrary number of processors.

Balancing Computational Load Among Processors for Parallel Calculationof R-Matrix

As a result of the following symmetry condition, only half of theR-matrix elements need to be explicitly calculated:R _(lk)(m)=ξR _(k,l)(−m).  (39)

In essence, only two matrices need to be calculated. One of thesematrices is combination of R(1) and R(−1), and the other is the R(0)matrix. In this case, the essential R(0) matrix elements have atriangular structure. The number of computations performed to generatethe raw data for the R(1)/R(−1) and R(0) matrices are combined andoptimized as a single number. This approach is adopted due to the reuseof the X matrix outer product values (see the above Equation (8)) acrossthe two R-matrices. Combining the X matrix and correlation valuesdominate the processor utilization since they represent the bulk of thecomputations. In this embodiment, these computations are employed as acost metric for determining the optimum loading of each processor.

The optimization problem can be formulated as an equal area problem,where the solution results in equal partition areas. Since the majordimensions of the R-matrices are given in terms of the number of activevirtual users, the solution space for the optimization problems can bedefined in terms of the number of virtual users per processor. It isclear to those skilled in the art that the solution can be applicable toan arbitrary number of virtual users by normalizing the solution spaceby the number of virtual users.

With reference back to FIG. 10, the computations of the R(1)/R(−1)matrix can be represented by a square HJKM while the computations of theR(0) matrix can be represented by a triangle ABC. From elementarygeometry, the area of a rectangle of length b and height h is given by:A _(r) =bh  (40)

and the area of a triangle with a base width b and a height h is givenby

$\begin{matrix}{A_{i} = {\frac{1}{2}{{bh}.}}} & (41)\end{matrix}$

Accordingly, a combined area of a rectangle A_(ri) and a triangle A_(ti)having a common height a_(i) is given by the following relation:

$\begin{matrix}\begin{matrix}{A_{i} = {A_{ri} + A_{ti}}} \\{= {{a_{i}a_{3}} + {\frac{1}{2}{a_{i}^{2}.}}}} \\{= {a_{i} + {\frac{1}{2}a_{i}^{2}}}}\end{matrix} & (42)\end{matrix}$

wherein A_(i) provides the area of a region below a given partitionline. For example, A₂ provides the area within the rectangle HQRM plusthe region within triangle AFG. The difference in the area of successivepartition regions is employed to form a cost function. Moreparticularly,

$\begin{matrix}\begin{matrix}{B_{i} = {A_{i} - A_{i - 1}}} \\{= {{\frac{1}{2}a_{i}^{2}} + a_{i} - {\frac{1}{2}a_{i - 1}^{2}} - a_{i - 1}}}\end{matrix} & (43)\end{matrix}$

For an optimum solution, B_(i)'s corresponding to i=1, 2, . . . , N,where N is the number of processors performing the calculations, areequal. Because the total normalized load is equal to A_(N), the load perprocessor is equal to A_(N)/N. That is

$\begin{matrix}{{B_{i} = {\frac{A_{N}}{N} = {\frac{A_{3}}{3} = \frac{3}{2N}}}},{{f\; o\; r\mspace{20mu} i} = 1},2,\ldots\;,{N.}} & (44)\end{matrix}$

By combining the above equations for B_(i), the solution for a_(i) canbe found by finding the roots of the following equation:

$\begin{matrix}{{{\frac{1}{2}a_{i}^{2}} + a_{i} - {\frac{1}{2}a_{i - 1}^{2}} - a_{i - 1} - \frac{3}{2N}} = 0.} & (45)\end{matrix}$

Hence, the solution of a_(i) is given as follows:

$\begin{matrix}{{a_{i} = {{- 1} \pm \sqrt{1 + a_{i - 1}^{2} + {2a_{i - 1}} + \frac{3}{N}}}},} & (46)\end{matrix}$

The negative roots of the above solution for a_(i) are discarded becausethe solution space falls in a range [0,1]. Although it appears that asolution of a_(i) requires first obtaining values of a_(i)−1, expandingthe recursion relations of the a_(i) and utilizing the fact that a₀equals 0 results in obtaining the following solution for a_(i) that doesnot require obtaining a_(i)−1:

$\begin{matrix}{a_{i} = {{- 1} + \sqrt{1 + \frac{3i}{N}}}} & (47)\end{matrix}$

The table below illustrates the normalized partition values of two,three, and four processors. To calculate the actual partition values,the number of active virtual users is multiplied by the correspondingtable entries. Since a fraction of a user can not be allocated, aceiling operation can be performed that biases the number of virtualusers per processor towards the processors whose loading function isless sensitive to perturbations in the number of users

Location Two processors Three processors Four processors a₁${- 1} = {\frac{5}{2}(0.5811)}$ ${- 1} + {\sqrt{2}(0.4142)}$${- 1} + {\sqrt{\frac{7}{4}}(0.3229)}$ a₂ — ${- 1} + {\sqrt{3}(0.7321)}$${- 1} + {\sqrt{\frac{5}{2}}(0.5811)}$ a₃ — —${- 1} + {\sqrt{\frac{13}{4}}(0.8028)}$

The above methods for calculating the R-matrix elements can beimplemented in hardware and/or software as illustrated elsewhere herein.With reference to FIG. 20, in one embodiment, the above calculations areperformed by utilizing a single card that is populated with four PowerPC 7410 processors. These processors employ the AltiVec SIMD vectorarithmetic logic unit which includes 32 128-bit vector registers. Theseregisters can hold either four 32-bit float, or four 32-bit integers, oreight 16-bit shorts, or sixteen 8-bit characters. Two vector SIMDoperations can be performed by clock. The clock rate utilized in thisembodiment is 400 Mz, although other clock rates can also employed. Eachprocessor has 32 KB of L1 cache and 2 MB of 266 MHz L2 cache. Hence, themaximum theoretical performance level of these processors is 3.2 GFLOPS,6.4 GOPS (16-bit), or 12.8 GOPS (8-bit). In this exemplary embodiment, acombination of floating-point, 16-bit fixed-point and 8-bit fixed-pointcalculations are utilized.

With continued reference to FIG. 20, the calculation of the C-matrixelements are performed by a single processor 220. In contrast, thecalculation of the R-matrix elements are divided among three processors222, 224, and 226. Further, a RACE++ 266 MB/sec 8-port switched fabric228 interconnects the processors. The high bandwidth of the fabricallows transfer of large amounts of data with minimal latency so as toprovide efficient parallelism of the four processors.

Vector Processor-Based R-Matrix Generation

Vector processing is beneficially employed, in one embodiment of theinvention, to speed calculations performed by the processor card ofFIGS. 2 and 3. Specifically, the AltiVec™ vector processing resources(and, more particularly, instruction set) of the Motorola PowerPC 7400processor used in node processors 228 are employed to speed calculationof the R-matrix. These processors include a single-instructionmultiple-data (SIMD) vector arithmetic logic unit which includes 32128-bit input vector units. These units can hold either four 32-bitintegers, or eight 16-bit integers, or even sixteen 8-bit integers. Theclock rate utilized in this embodiment is 400 Mz, although other clockrates can be also employed.

Of course, those skilled in the art will appreciate that other vectorprocessing resources can be used in addition or instead. These caninclude SIMD coprocessors or node processors based on other chip sets,to name a few. Moreover, those skilled in the art will appreciate that,while the discussion below focuses on use of vector processing to speedcalculation of the R-matrix, the techniques described below can beapplied to calculating other matrices of the type described previouslyas well, more generally, to other calculations used for purposes of CDMAand other communications signal processing.

In the illustrated embodiment, a mapping vector is utilized to create amapping between each physical user and its associated (or “decomposed”)virtual users. This vector is populated during the decomposition processwhich, itself, can be accomplished in a conventional manner known in theart. The vector is used, for example, during generation of the R-matrixas described below.

As further evident in the discussion below, the X-matrix (see Equation(8)), is arranged such that a “strip-mining” method of the boundaryelements can be performed to further increase speed and throughput. Theelements of that matrix are arranged such that successive ones of themcan be stripped to generate successive elements in the R-matrix. Thispermits indices to be incremented rather than calculated. The elementsarc, moreover, arranged in a buffer such that adjacent elements can bemultiplied with adjacent element of the C-matrix, thereby, limiting thenumber of required indices to two within the iterative summation loops.

In the discussion that follows, a node processor 228 operating as avector processor is referred to as vector processor 410. FIG. 21 is ablock diagram depicting the architecture and operation of one such nodeprocessor 228, and its corresponding vector processor 410, used in anembodiment of the invention to calculate the R-matrix 428 using integerrepresentations of the C-matrix 424 and waveform amplitudes 426. Tofacilitate a complete understanding of the illustrated embodiments, onlya sampling of operands are illustrated, e.g., a few elements each of theC-matrix 424, complex amplitudes 426 and R-matrix 428. In actualoperation of a system according to the invention, the vector processor410 can used to process matrices containing hundreds or thousands ofelements.

As shown in the drawing, the illustrated node processor 228 isconfigured via software instructions to execute a floating point tointeger transformation process 406 and an integer to floating pointtransformation process 412, well as to serve as a vector processor 410.The relationship and signalling between these modes is depicted in thedrawing.

By way of overview, and as discussed above, one or more code-divisionmultiple access (CDMA) waveforms or signals transmitted, e.g., from auser cellular phone, modem or other CDMA signal source are decomposedinto one or more virtual user waveforms. The virtual user is deemed to“transmit” a single bit per symbol period of that received CDMAwaveform. In turn, each of the virtual user waveforms is processedaccording to the methods and systems described above.

In some embodiments, waveform processing is performed usingfloating-point math, e.g., for generating the gamma-matrix, C-matrix,R-matrix, and so on, all in the manner described above. However, in anembodiment of the invention, e.g., reflected in FIG. 21, integer math isperformed on the vector processor 410, taking advantage ofblock-floating point representation of the operands. This speedswaveform processing, albeit at the cost of accuracy. However, in theillustrated embodiment, a balance is achieved by through use of 16-bitblock-floating point representation, e.g., in lieu of conventional32-bit floating-point representations. Those skilled in the art willappreciate that block-floating representations of other bit widths couldbe used instead, depending on implementation requirements.

Referring to FIG. 21, the C-matrix 424 is generated by the nodeprocessor 228 as described above, and is stored in memory accordingly ina floating-point representation, e.g., C₀ 401, C₁ 402, and so on.Further, the amplitudes 426 are stored in memory as floating-pointrepresentations. Both sets of representations are transformed intofloating-block format via a transformation process 406 which generates acommon exponent 414 and a 16-bit integer for each operand. Thetransformation process 416 stores two integers in each word, e.g., C₀408 a, C₁ 408 b, and a₀ 409 a, a₁ 409 b, and the corresponding blockexponent 414. The transformation process 414 can be performed viaspecial purpose function or through use of extensions to the Cprogramming language, as can be seen in a programming listing that isfurther described. The integers stored in memory, e.g., 408, 409, aremoved by the transformation process 406 to the vector processor 410 forprocessing.

The vector processor 410 includes two input vector units 416, 418, anoutput vector unit 420, and an arithmetic processor 422. Each vectorunit is 128-bits in length, hence, each can store eight of the 16-bitinteger operands. The arithmetic processor 422 has a plurality ofoperating elements, 422 a through 422 c. Each of the operating element422 a through 422 c applies functionality to a set of operands stored inthe input vector units 416, 418, and stores that processed data in theoutput vector 420. For example, the operating element 422 a performsfunctionality on operands C₀ 416 a and a₀ 418 a and generates R₀ 420 a.The arithmetic processor 422 can be programed via C programminginstructions, or by a field programmable gate array or other logic.

Although vector processor 410 includes two input vector units 416, 418,in other embodiments it can have numerous vector units, that can beloaded with additional C-matrix and complex amplitude representations atthe same time. Further, the operands can be stored in a non-sequentialorder to accommodate increased throughput via storing operands accordingto a first-used order.

As noted above, one way to program the arithmetic processor 422 isthrough extensions to a high level programming language. One suchprogram, written in C, suitable for instruction the vector processor 422to generate the R-matrix is as follows:

#include “mudlib.h” #define DO_CALC_STATS 0 #define DO_TRUNCATE 1#define DO_SATURATE 1 #define DO_SQUELCH 0 #define SQUELCH_THRESH 1.0#define TRUNCATE_BIAS 0.0 #if DO_TRUNCATE #define SATURATE_THRESH(128.0 + TRUNCATE_BIAS) #else #define SATURATE_THRESH 127.5 #endif#define SATURATE( f ) \ {  \ if ( (f) >= SATURATE_THRESH ) f =(SATURATE_THRESH − 1.0); \ else if ( (f) < −SATURATE_THRESH ) f =−SATURATE_THRESH; \ } #if DO_TRUNCATE #if 0 #define BF8_FIX( f ) ((BF8)(FABS(f) <= TRUNCATE_BIAS) ? 0 : \      (((f) > 0.0) ? ((f) − TRUNCATEBIAS) : \        ((f) + TRUNCATE_BIAS))) #define BF8_FIX( f ) ((BF8)(f)) #else #define BF8_FIX( f ) ((BF8) (((((f) < 0.0)) && ((f) ==(float) ((int) (f)))) ?\      ((f) + 1.0) : (f))) #endif #else #defineBF8_FIX( f ) ((BF8) (((f) >= 0.0) ? ((f)+0.5) : ((f)−0.5))) #endif#define UPDATE_MAX( f, max ) \ if ( FABS( f ) > max ) max = FABS( f );#define uchar unsigned char #define ushort unsigned short #define ulongunsigned long #if DO_CALC_STATS static float max_R_value; #endif voidgen_X_row ( COMPLEX_BF16 *mpath1_bf, COMPLEX_BF16 *mpath2_bf,COMPLEX_BF16 *X_bf, int phys_index, int tot_phys_users  ); voidgen_R_sums ( COMPLEX_BF16 *X_bf, COMPLEX_BF8 *corr_bf, uchar *ptov_map,BF32 *R_sums, int num_phys_users ); void gen_R_sums2 ( COMPLEX_BF16*X_bf, COMPLEX_BF8 *corra_bf, COMPLEX_BF8 *corrb_bf, uchar *ptov_map,BF32 *R_sumsa, BF32 *R_sumsb, int num_phys_users ); void gen_R_matrices( BF32 *R_sums, float *bf_scalep, float *inv_scalep, float *scalep, BF8*no_scale_row_bf, BF8 *scale_row_bf, int num_virt_users  ); voidmudlib_gen_R ( COMPLEX_BF16 *mpath1_bf, /* ANTENNA DATA 1: TWO AMPLITUDE  DATA VALUES a hat FOR EACH USER   */ BCOMPLEX_BF16 *mpath2_bf, /*ANTENNA DATA 2 */ COMPLEX_BF8 *corr_0_bf, /* adjusted for startingphysical   user */ /* C MATRIX, I.E., C(0), SYMBOL YOU   ARE ON VERSUSOTHER SYMBOLS */ COMPLEX_BF8 *corr_1_bf, /* adjusted for startingphysical   user */ /* C MATRIX. THIS IS A VIRTUAL   USER BY VIRTUAL USERMATRIX.   EACH USER HAS 16 VALUES THAT   CORRELATE THAT USER TO OTHER  USERS */ uchar *ptov_map, /* no mare than 256 virts. per phys   */ /*MAPPING OF PHYSICAL TO   VIRTUAL USERS MAP. IN FURTHER   EMBODIMENTS,THIS COULD   DYNAMICALLY CHANGE AS USERS   ENTER INTO AND LEAVE SYSTEM*/ float *bf_scalep, /* scalar: always a power of 2 */ /* VECTOR WITHSCALAR FOR EACH   VIRTUAL USER −− NOTWITHSTANDING   */ float*inv_scalep, /* start at 0'th physical user */ float *scalep, /* startat 0'th physical user */ char *L1_cachep, /* temp: 32K bytes, 32-bytealigned   */ /* OUTPUTS (BEGINNING AT NEXT LINE)   */ BF8 *R0_upper_bf,/* UPPER PART OF R(1) MATRIX −− A   TRIANGULAR PACKED MATRIX */ BF8*R0_lower_bf, /* LOWER PART OF R(0) MATRIX */. BF8 *R1_trans_bf, /*TRANSPOSED FORM OF R(0) */ BF8 *R1m_bf, /* R(−1) −−> “m” STANDS FOR −1*/ int tot_phys_users, /* TOTAL PHYSICAL USERS */ int tot_virt_users, /*SUM OF VIRTUAL USERS */ int start_phys_user, /* zero-based starting row  (inclusive) */ /* STARTING PHYSICAL USER TO WHICH   THIS PROCESSOR ISASSIGNED */ int start_virt_user, /* relative to start_phys_user */ /*STARTING VIRTUAL USER TO WHICH   THIS PROCESSOR IS ASSIGNED */ /* NOTE:THIS IS AN ADVANTAGE   IN ALLOWING US TO PARTITION A   GIVEN PHYSICALUSER TO MULTIPLE   PROCESSORS */ int end_phys_user, /* zero-based endingrow inclusive)   */ /* SAME AS ABOVE, BUT END VALUES */ intend_virt_user /* relative to end_phys_user */  ) { COMPLEX_BF16 *X_bf;BF32 *R_sums0, *R_sums1; /* BEGINNING OF PARTITIONING AND   PARAMETERSET-UP LOGIC */ uchar *R0_ptov_map; int bump, byte_offset, i, iv,last_virt_user; int R0_align, R0_skipped_virt_users, R0_tcols,R0_virt_users, R1_tcols; #if DO_CALC_STATS max_R_value = 0.0; #endifX_bf = (COMPLEX_BF16 *)L1_cachep; byte_offset = tot_phys_users *NUM_FINGERS_SQUARED * sizeof(COMPLEX_(—)    BF16); R_sums0 = (BF32 *)(((ulong)X_bf + byte_offset + R_MATRIX_ALIGN_MASK) &   ~R_MATRIX_ALIGN_MASK); byte_offset = tot_virt_users * sizeof(BF32);R_sums1 = (BF32 *) (((ulong)R_sums0 + byte_offset + R_MATRIX_ALIGN_MASK)&    ~R_MATRIX_ALIGN_MASK); R0_ptov_map = (uchar *) (((ulong) R_sums1 +byte_offset + R_MATRIX_ALIGN_(—)    MASK) & ~R_MATRIX_ALIGN_MASK);R1_tcols = (tot_virt_users + R_MATRIX_ALIGN_MASK) &~R_MATRIX_ALIGN_MASK; R0_virt_users = 0; for ( i = start_phys_user; i <tot_phys_users; i++ ) { R0_virt_users += (int)ptov_map[i]; R0_ptov_map[i] = ptov_map[i]; } R0_ptov_map[start_phys_user] −= start_virt_user;R0_skipped_virt_users = tot_virt_users − R0_virt_users +start_virt_user; R0_virt_users −= (start_virt_user + 1); −−inv_scalep;/* predecrement to allow for common  indexing */ for ( i =start_phys_user; i <= end_phys_user; i++ ) { /* LOOP OVER ALL PHYSICALUSERS (ASSIGNED TO THIS PROCESSOR) */ gen_X_row (     /* FIND C CODETHAT PERTAINS TO THIS */ mpath1_bf, mpath2_bf, X_bf, i, tot_phys_users); −−R0_ptov_map[i];  /* excludes R0 diagonal */ last_virt_user = (i <end_phys_user) ? ((int)ptov_map[i] − 1) :          end_virt_user; for (iv = start_virt_user; (iv + 1) <= last_virt_user; iv += 2 ) {gen_R_sums2 ( X_bf + (i * NUM_FINGERS_SQUARED), corr_0_bf, corr_0_bf +((R0_virt_users − 1) * NUM_FINGERS_SQUARED), R0_ptov_map + i, R_sums0 +(R0_skipped_virt_users + 1), R_sums1 + (R0_skipped_virt_users + 1),tot_phys_users − i ); R0_tcols = R1_tcols − (R0_skipped_virt_users &~R_MATRIX_ALIGN_MASK); R0_align = (R0_skipped_virt_users &R_MATRIX_ALIGN_MASK) + 1; gen_R_matrices ( R_sums0 +(R0_skipped_virt_users + 1), bf_scalep, inv_scalep+(R0_skipped_virt_users + 1), scalep + (R0_skipped_virt_users + 1),R0_lower_bf + R0_align, R0_upper_bf + R0_align, R0_virt_users );R0_upper_bf[ R0_align − 1 ] = 0; /* zero diagonal element */ R0_lower_bf+= R0_tcols; R0_upper_bf += R0_tcols; R0_tcols = R1_tcols −((R0_skipped_virt_users + 1) &        ~R_MATRIX_ALIGN_MASK); R0_align =((R0_skipped_virt_users + 1) & R_MATRIX_ALIGN_MASK) + 1; gen_R_matrices( R_sums1 + (R0_skipped_virt_users + 2), bf_scalep, inv_scalep +(R0_skipped_virt_users + 2), scalep + (R0_skipped_virt_users + 2),R0_lower_bf + R0_align, R0_upper_bf + R0_align, R0_virt_users − 1 );R0_upper_bf[ R0_align − 1 ] = 0; /* zero diagonal element */ R0_lower_bf+= R0_tcols; R0_upper_bf += R0_tcols; /*  * create ptov_map[i] number of32-element dot products involving  * X_bf[i] and corr_1_bf[i][j] where 0< j < ptov_map[i]  */ gen_R_sums2 ( X_bf, corr_1_bf, corr_1_bf +(tot_virt_users * NUM_FINGERS_SQUARED), ptov_map, R_sums0, R_sums1,tot_phys_users ); /*  * scale the results and create two output rows (1per matrix)  */ gen_R_matrices ( R_sums0, bf_scalep, inv_scalep +(R0_skipped_virt_users + 1), scalep, R1_trans_bf, R1m_bf, tot_virt_users); R1_trans_bf += R1_tcols; R1m_bf += R1_tcols; gen_R_matrices (R_sums1, bf_scalep, inv_scalep + (R0_skipped_virt_users + 2), scalep,R1_trans_bf, R1m_bf, tot_virt_users ); R1_trans_bf += R1_tcols; R1m_bf+= R1_tcols; corr_0_bf += (((2 * R0_virt_users) − 1) *NUM_FINGERS_SQUARED); corr_1_bf += ((2 * tot_virt_users) *NUM_FINGERS_SQUARED); R0_ptov_map[i] −= 2; R0_virt_users −= 2;R0_skipped_virt_users += 2; } if ( iv <= last_virt_user ) { bump =R0_ptov_map[ i ] ? 0 : 1; gen_R_sums ( X_bf + ((i + bump) *NUM_FINGERS_SQUARED), corr_0_bf, R0_ptov_map + i + bump, R_sums0 +(R0_skipped_virt_users + 1), tot_phys_users − i − bump ); R0_tcols =R1_tcols − (R0_skipped_virt_users & ~R_MATRIX_ALIGN_MASK); R0_align =(R0_skipped_virt_users & R_MATRIX_ALIGN_MASK) + 1; gen_R_matrices (R_sums0 + (R0_skipped_virt_users + 1), bf_scalep, inv_scalep +(R0_skipped_virt_users + 1), scalep + (R0_skipped_virt_users + 1),R0_lower_bf + R0_align, R0_upper_bf + R0_align, R0_virt_users );R0_upper_bf[ R0_align − 1 ]= 0; /* zero diagonal element */ R0_lower_bf+= R0_tcols; R0_upper_bf += R0_tcols; /*  * create ptov_map[i] number of32-element dot products involving  * X_bf[i] and corr_1_bf[i][j] where 0< j < ptov_map[i]  */ gen_R_sums ( X_bf, corr_1_bf, ptov_map, R_sums0,tot_phys_users ); /*  * scale the results and create two output rows (1per matrix)  */ gen_R_matrices ( R_sums0, bf_scalep, inv_scalep +(R0_skipped_virt_users + 1), scalep, R1_trans_bf, R1m_bf, tot_virt_users); R1_trans_bf += R1_tcols; R1m_bf += R1_tcols; corr_0_bf +=(R0_virt_users * NUM_FINGERS_SQUARED); corr_1_bf += (tot_virt_users *NUM_FINGERS_SQUARED); R0_ptov_map[i] −= 1; R0_virt_users −= 1;R0_skipped_virt_users += 1; } start_virt_user =0;    /* for allsubsequent passes */ } #if DO_CALC_STATS printf( “max_R_value = %f\n”,max_R_value ); if ( max_R_value > 127.0 ) printf ( “***** OVERFLOW*****\n” ); #endif } #if COMPILE_C /* OUTPUT PRODUCT OF TWO  ANTENNAS */void gen_X_row ( /* EACH ANTENNA HAS TWO  VALUES PER PHYSICAL USER  */COMPLEX_BF16 *mpath1_bf, /* 2ND ANTENNA IS DIVERSITY ANTENNA */COMPLEX_BF16 *mpath2_bf, /* RESULTING OUTPUT PRODUCT IS REP'D BY  X subl,k */ COMPLEX_BF16 *X_bf, int phys_index, int tot_phys_users ) {COMPLEX_BF16 *in_mpath1p, *in_mpath2p; COMPLEX_BF16 *out_mpath1p,*out_mpath2p; int i, j, q, q1; BF32 s1r, s1i, s2r, s2i; BF32 a1r, a1i,a2r, a2i; BF32 cr, ci; out_mpath1p = mpath1_bf + (phys_index *NUM_FINGERS); out_mpath2p = mpath2_bf + (phys_index * NUM_FINGERS); for( i = 0; i < tot_phys_users; i++ ) { in_mpath1p = mpath1_bf + (i *NUM_FINGERS);   /* 4 complex values */ in_mpath2p = mpath2_bf + (i *NUM_FINGERS);   /* 4 complex values */ j = 0; for ( q1 = 0; q1 <NUM_FINGERS; q1++ ) { s1r = (BF32) out_mpath1p[q1].real; s1i = (BF32)out_mpath1p[q1].imag; s2r = (BF32) out_mpath2p[q1].real; s2i = (BF32)out_mpath2p[q1].imag; for ( q = 0; q < NUM_FINGERS; q++ ) { a1r = (BF32)in_mpath1p[q].real; a1i = (BF32) in_mpath1p[q].imag; a2r = (BF32)in_mpath2p[q].real; a2i = (BF32) in_mpath2p[q].imag; cr = (a1r * s1r) +(a1i * s1i); /* COMBO OF TWO ANTENNAS −−  COULD BE MORE, OF COURSE  */ci = (a1r * s1i) = (a1i * s1r); /* cr IS REAL PART OF  ELEMENT OFX-MATRIX */ cr += (a2r * s2r) + (a2i * s2i); ci += (a2r * s2i) − (a2i *s2r); X_bf[i * NUM_FINGERS_SQUARED + j].real = (BF16) (cr >> 16); /*BLOCK X_bf[i * NUM_FINGERS_SQUARED + j].imag = (BF16) (ci >> 16); ++j; }} } } void gen_R_sums ( COMPLEX_BF16 *X_bf, COMPLEX_BF8 *corr_bf, uchar*ptov_map, BF32 *R_sums, int num_phys_users ) { int i, j, k; BF32 sum;for ( i = 0; i < num_phys_users; i++ ) { for ( j = 0; j <(int)ptov_map[i]; j++ ) { sum = 0; for ( k = 0; k < 16; k++ ) { sum +=(BF32) X_bf[k].real * (BF32) corr_bf−>real; sum += (BF32) X_bf[k].imag *(BF32) corr_bf−>imag; ++corr_bf; } *R_sums++ = sum; } X_bf +=NUM_FINGERS_SQUARED; } } void gen_R_sums2 ( COMPLEX_BF16 *X_bf,COMPLEX_BF8 *corra_bf, COMPLEX_BF8 *corrb_bf, uchar *ptov_map, BF32*R_sumsa, BF32 *R_sumsb, int num_phys_users ) { int i, j, k; BF32 suma,sumb; for ( i = 0; i < num_phys_users; i++ ) { for ( j = 0; j <(int)ptov_map[i]; j++ ) { suma = 0; sumb = 0; for ( k = 0; k < 16; k++ ){ suma += (BF32) X_bf[k].real * (BF32) corra_bf−>real; suma += (BF32)X_bf[k].imag * (BF32) corra_bf−>imag; sumb += (BF32) X_bf[k].real *(BF32) corrb_bf−>real; sumb += (BF32) X_bf[k].imag * (BF32)corrb_bf−>imag; ++corra_bf; ++corrb_bf; } *R_sumsa++ = suma; *R_sumsb++= sumb; } X_bf += NUM_FINGERS_SQUARED; } } void gen_R_matrices ( BF32*R_sums, float *bf_scalep, float *inv_scalep, float *scalep, BF8*no_scale_row_bf, BF8 *scale_row_bf, int num_virt_users ) { int i; floatbf_scale, fsum, fsum_scale, inv_scale, scale; bf_scale = *bf_scalep;inv_scale = *inv_scalep; for ( i = 0; i < num_virt_users; i++ ) { scale= scalep[i]; fsum = (float) (R_sums[i]); fsum *= bf_scale; fsum_scale =fsum * inv_scale; fsum_scale *= scale; #if DO_CALC_STATS UPDATE_MAX(fsum_scale, max_R_value ) UPDATE_MAX( fsum, max_R_value ) #endif #ifDO_SQUELCH if ( FABS( fsum_scale ) <= SQUELCH_THRESH ) fsum_scale = 0.0;if ( FAES( fsum) <= SQUELCH_THRESH ) fsum = 0.0; #endif #if DO_SATURATESATURATE ( fsum_scale ) SATURATE ( fsum ) #endif no_scale_row_bf[i] =BF8_FIX( fsum ); scale_row_bf[i] = BF8_FIX( fsum_scale ); } }#endif       /* COMPILE_C */

A transformation process 412 transforms the block-floatingrepresentations stored in the output vector unit 420 into floating pointrepresentations and stores those to a memory 428. Here, the R-matrixelements stored in the output vector unit 420 are transformed intofloating-point representations, which can then be used in the mannerdescribed above for estimating symbols in the physical user waveforms.

In summary, sufficient throughput can be achieved with necessaryaccuracy using a vector processor 410 applying integer math on 16-bitblock-floating integers. Of course, in other embodiments, differentblock-floating sizes can be used depending on such criteria as thenumber of users, speed of the processors, and necessary accuracy of thesymbol estimates, to name a few. Further, like methods and logicdescribed can be used to generate other matrices (e.g., the gamma-matrixand the C-matrix) and to perform other calculations within theillustrated embodiment.

A further understanding of the operation of the illustrated and otherembodiments of the invention may be attained by reference to (i) U.S.Provisional Application Ser. No. 60/275,846 filed Mar. 14, 2001,entitled “Improved Wireless Communications Systems and Methods”; (ii)U.S. Provisional Application Ser. No. 60/289,600 filed May 7, 2001,entitled “Improved Wireless Communications Systems and Methods UsingLong-Code Multi-User Detection'” and (iii) U.S. Provisional ApplicationSer. No. 60/295,060 filed Jun. 1, 2001 entitled “Improved WirelessCommunications Systems and Methods for a Communications Computer,” theteachings all of which are incorporated herein by reference, and a copyof the latter of which may be filed herewith.

The above embodiments are presented for illustrative purposes only.Those skilled in the art will appreciate that various modifications canbe made to these embodiments without departing from the scope of thepresent invention. For example, the processors could be of makes andmanufactures and/or the boards can be of other physical designs, layoutsor architectures. Moreover, the FPGAs and other logic devices can besoftware or vice versa. More over, it will be appreciated that while theillustrated embodiments decomposes physical user waveforms to virtualuser waveforms, the mechanisms described herein can be applied, as well,without such decomposition, and that, accordingly, the terms “waveform”or “user wave-form” should be treated as referring to either physical orvirtual waveforms unless otherwise evident from context.

1. A method of processing spread spectrum waveforms transmitted by aplurality of users of a spread spectrum system, comprising distributingamong a plurality of logic units parallel tasks each for computing aportion of a matrix indicative of cross correlations among the waveformstransmitted by the users, partitioning computation of thecross-correlation matrix such that a computational load associated witha task distributed to one of said logic units is substantially equal tocomputational load associated with another task distributed to anotherlogic unit, executing with the plurality of logic units the distributedtasks, generating detection statistics corresponding to symbolstransmitted by the users and encoded in the waveforms as a function ofthe cross correlation matrix, and generating estimates of the symbolsbased on the detection statistics.
 2. The method of claim 1, furthercomprising the step of defining a metric associated with each partitionin accord with the relation:B _(i) =A _(i) −A _(i−1) wherein A_(i) represents an area of a portionof the cross-correlation matrix corresponding to the ith partition, andi represents an index corresponding to the number of logic units.
 3. Themethod of claim 2, further comprising the step of representing thecross-correlation matrix as a composition of a rectangular component anda triangular component.
 4. The method of claim 3, wherein each areaA_(i) includes a first portion corresponding to the rectangularcomponent and a second portion corresponding to the triangular componentof the cross-correlation matrix.
 5. The method of claim 4, wherein thestep of partitioning the matrix includes selecting the matrix associatedwith the partitions to be substantially equal.
 6. The method of claim 3,wherein the cross-correlation matrix is computed as a composition of afirst component that represents correlations among time lags and codesequences associated with the waveforms transmitted by the users and asecond component that represents correlations among multipath signalamplitudes associated with the waveforms transmitted by the users.
 7. Amethod of processing spread spectrum waveforms transmitted by aplurality of users of a spread spectrum system, comprising partitioningcomputation of a matrix representing cross-correlations among thewaveforms transmitted by the users in accord with a pre-defined metric,distributing among a plurality of logic units parallel tasks eachcorresponding to one of said partitions for computing a portion of thematrix, executing with the plurality of logic units the distributedtasks, assembling said computed portions to generate thecross-correlation matrix, representing the cross-correlation matrix as acomposition of a first component that represents correlations among timelags and code sequences associated with the waveforms transmitted by theusers and a second component that represents correlations amongmultipath signal amplitudes associated with the waveforms transmitted bythe users, generating detection statistics corresponding to symbolstransmitted by the users and encoded in the waveforms as a function ofthe cross correlation matrix, and estimating the symbols based on thedetection statistics.
 8. The method of claim 7, wherein the step ofpartitioning comprises defining the metric in accord with the relation:B _(i) =A _(i) −A _(i−1) wherein A_(i) represents an area of a portionof the cross-correlation matrix corresponding to the ith partition, andi represents an index corresponding to the number of logic units.
 9. Amethod of processing spread spectrum waveforms transmitted by aplurality of users of a spread spectrum system, comprising partitioningcomputation of a matrix representing cross-correlations among thewaveforms transmitted by the users in accord with a pre-defined metric,distributing among a plurality of logic units parallel tasks eachcorresponding to one of said partitions for computing a portion of thematrix, executing with the plurality of logic units the distributedtasks, assembling said computed portions to generate thecross-correlation matrix, representing the cross-correlation matrix as acomposition of a first component that represents correlations among timelags and code sequences associated with the waveforms transmitted by theusers and a second component that represents correlations amongmultipath signal amplitudes associated with the waveforms transmitted bythe users, generating detection statistics corresponding to symbolstransmitted by the users and encoded in the waveforms as a function ofthe cross correlation matrix, and generating estimates of the symbolsbased on the detection statistics wherein correlations among the codesequences associated with the respective users are computed in accordwith the relation:${\Gamma_{l\; k}\lbrack m\rbrack} \equiv {\frac{1}{2N_{l}}{\sum\limits_{n = 0}^{N - 1}{{c_{l}^{*}\lbrack n\rbrack} \cdot {c_{k}\left\lbrack {n - m} \right\rbrack}}}}$wherein Γ_(lk)[m] represents correlation between l and k user codescorresponding to a shift of m chips, c^(*) _(l)[n] represents complexconjugate of the code sequences associated with the lth user, c_(k)[n−m]represents the code sequences associated with kth user, N represents thelength of the code, and N_(l) represent the number of non-zero length ofthe code.
 10. The method of claim 9, further comprising the step ofcomputing the first component of the cross correlation matrix as amatrix component (herein referred to as C matrix) in accord with therelation:${C_{l\; k\; q\; q} \cdot \left\lbrack m^{\prime} \right\rbrack} = {\sum\limits_{m}{{g\left\lbrack {{m\; N_{c}} + \tau} \right\rbrack} \cdot {\Gamma_{l\; k}\lbrack m\rbrack}}}$wherein g is a pulse shape vector, N_(c) is the number of samples perchip, τ is a time lag, and Γ_(lk)[m] represents correlation between land k user codes corresponding to a shift of m chips.
 11. The method ofclaim 10, further comprising the step of computing the cross-correlationmatrix (herein referred to as r matrix) in accord with the relation:${r_{lk}\left\lbrack m^{\prime} \right\rbrack} = {{\sum\limits_{q = 1}^{L}{\sum\limits_{q^{\prime} = 1}^{L}{R\; e\left\{ {{\hat{a}}_{l\; q}^{*}{a_{k\; q} \cdot C_{{l\; k\; q\; q}\;} \cdot \left\lbrack m^{\prime} \right\rbrack}} \right\}}}} = {R\; e\left\{ {a_{l}^{H} \cdot {C_{l\; k}\left\lbrack m^{\prime} \right\rbrack} \cdot a_{k}} \right\}}}$wherein â_(lq) ^(*) is an estimate of α_(lq) ^(*), which represents acomplex conjugate of one multipath amplitude component of the 1 ^(th)user, α_(kq), is one multipath amplitude component associated with thek^(th) user, and C denotes the aforesaid C matrix.
 12. The method ofclaim 11, wherein the step of generating detection statistics comprisescomputing the detection statistics in accord with the relation:${y_{l}\lbrack m\rbrack} = {{{r_{l\; l}\lbrack 0\rbrack}{b_{l}\lbrack m\rbrack}} + {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\left\lbrack {- 1} \right\rbrack}{b_{k}\left\lbrack {m + 1} \right\rbrack}}} + {\sum\limits_{k = 1}^{K_{v}}{\left\lbrack {{r_{l\; k}\lbrack 0\rbrack} - {{r_{l\; l}\lbrack 0\rbrack}\delta_{l\; k}}} \right\rbrack{b_{k}\lbrack m\rbrack}}} + {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\lbrack 1\rbrack}{b_{k}\left\lbrack {m - 1} \right\rbrack}}} + {\eta_{l}\lbrack m\rbrack}}$wherein y_(l)[m] represents detection statistic for the mth symboltransmitted by the lth user, r_(ll)[0]b_(l)[m] represents a signal ofinterest, and remaining terms of the relations represent Multiple AccessInterference (MAI) and noise.
 13. The method of claim 12, wherein thestep of generating symbol estimates comprises computing the estimates inaccord with the relation:${{\hat{b}}_{l}\lbrack m\rbrack} = {s\; i\; g\; n\left\{ {{y_{l}\lbrack m\rbrack} - {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\left\lbrack {- 1} \right\rbrack}{{\hat{b}}_{k}\left\lbrack {m + 1} \right\rbrack}}} - {\sum\limits_{k = 1}^{K_{v}}{\left\lbrack {{r_{l\; k}\lbrack 0\rbrack} - {{r_{l\; l}\lbrack 0\rbrack}\delta_{l\; k}}} \right\rbrack{{\hat{b}}_{k}\lbrack m\rbrack}}} - {\sum\limits_{k = 1}^{K_{v}}{{r_{l\; k}\lbrack 1\rbrack}{{\hat{b}}_{k}\left\lbrack {m - 1} \right\rbrack}}}} \right\}}$wherein {circumflex over (b)}_(l)[m] represents an estimate of the mthsymbol transmitted by the lth user, g is a pulse shape vector, N_(c) isthe number of samples per chip, τ is a time lag, and Γ represents the Γmatrix.